Sorry for the late reply. I think I understand where you're coming from: there's a feeling of powerleness for issues that you really care about, and that's really bringing you down. I have 3 points to cover.
1)Humans have evolved to be tribalistic. Shutting outsiders out is a tale as old as time, and it's related to how people tend to process things. The human mind learns how to deal with certain issues, as well as gaining what they want, through so-called "control theories". It's a set of case-by-case instructions that we learn as kids through experience, exposure to adults, traditions, religions, etc... and our brains from them with the prupose to make sure we have a place in our community. Among these control theories there are shared ones, which are basically the rules (spoken or unspoken) of our community, that teach use how to survive and gain status in our environment. They're convenient, pre-packaged control theories that firmly lodge themselves in our mental tools for surviving, and therefore identity. Political ideologies are an example of this.
Now, our brains have the etendency to identify with those control theories. It makes sense, because--like I said--those are our ways to keep existing in a decent enough way. That means that a threat to them is provessed by our brain as a threat to us as individuals and to our survival. There have been fMRI scans run on people whose political ideology was challegned, and the centers that respond to physical aggressions lit up. It's insane, but it explains so much of what we see around us. Now, the subtext of a sizable influx of migrants is that of a new control theory coming in, as our communities mix up and therefore their rules also do. That means that people's brain go full "wait, the presnece of these migrants means that our control theory is changing and no longer valid. They're threatening our way to survive. They're a threat to us!" So, they will come up with all sorts of rationalizations (grounded in reality or not) to justify refusing those migrants. They represent a huge canage, and that's scary. Does that justify closure? Nope, but it explains it, and it alos explains that people don't even realize the reason why they're doing it, because we can hardly see the world outside of our control theories, and it takes a special kind of education in order to even realize that you're watching the world through the lenses of your control theories, let alone take those lenses off and view the world through both logic and compassion. It's really hard.
A good merging of 2 cultures requires to ahve some big priorities in common. Once you establish that the goals fo the 2 sides have overlapping, and that there are principles that both sides share, you can work from there. There has to be a basis of shared interest for that to happen. However, you as an individual pbviously can't do this on a large scale. So, why am I telling you this? Because, if you want to do something about migrants and not lose your mental wellbeing over it, that's something we all have to accept how the human brain works first. You will hardly find a country that, as a whole, just openly welcomes migrants. The problem you've shown me basically stems from you feeling powerless about something that deeply affects you on an emotional level. What to do about powerlessness? Find something that you can do immediately.
You will hardly make a large scale change by yourself, and ypu will most likely be unable to change people. If you accept this, and set your expectations to a doable level, you can prevent the vastity of the problem overwhelm you, and look for stuff you can affect with a mind that isn't weighed down by the feeling of powerlessness. The only way to change this, is educating young people in schools about the inner workings of our brains, their trappings, and how to catch those mechanisms and not let them control it. Aka, crouses about practical applications of neurosciences&psychology. That's the best thing a government can do: strike the problem at its root.
What YOU can do? Look at what's going on near you. Are there migrants in need of help in your city? If so, you can go there and help, like Eilistraee teaches, in practical ways--cooking food, help tending to shelters, etc... (dw, I didn't forget you have social anxiety, I'll cover that in point 2). If you want to stay more "at range", you can support organizations that protect migrants' rights (like Amnesty), or send supplies. If you can't afford that, you may want to try and see if there's any work you may be able to do for these organizations (writing newsletters, contacting people to explain the situation to them--if you feel comfortable with it, ofc--, etc...).
The best case scenario is managing to get physcially involved in stuff, as that will allow you to participate in building a local community that cares about this issue, and--like they say--"if you build it, they will come". Such a community will drag in more people and eventually even make them see stuff from a different perspective.
2)Be compassionate towards yourself. The feeling of powerlessness stems from being uable to create changes you want to see. Being able to change something for the better, in a way that immediately affects you, will help with that feeling of powerlessness even if it's not directly related to the change you want to see in your country. It will give you a tool to better and more comfortably act on the outside world, to withstand frustration and disappointment,and that's invaluable to get results. Basically, the less limits (such as social anxiety) on how you can act you have, the better you'll feel in regards to the various issues that are important to you. I don't know how healthcare works in Germany in terms of costs, but stuff like therapy, coaching (
https://www.healthygamer.gg/) can be a gamechanger. Even completing some personal project that's lying there unfinished, or completing small tasks, or starting with small interactions with other people, can go a long way to reduce the feeling of powerlessness. Trying to understand
3)Understand where your need of helping abandoned people comes from, and which of your needs it's trying to satisfy. Granted, I'm not saying that compassion isn't anything but excellent, but like all behaviors in people, it's also born out of a purpose. You said you're unable to withhold compassion; that means your brain sees compassion as a "control theory" of sorts. Try asking yourself: "what would happen if I withheld compassion from someone?" and keep asking this question until you reach an answer that directly affects you.
Example:
"what would happen if I withheld compassion from someone?"
"that person would suffer, when I could have done something about it"
"and why would that affect me?"
"because that would make me a bad person"
"and why is being a bad person bad for me?"
"because then I would deserve to be rejected"
The control theory that we can deduce from this case goes somewhat like: "in order to be accepted, I need to be a giver".
What do we do with this info? Well, first off, we ask "is this a harmful control theory?" Not particularly (but remember that placing a condition, any condition, on you being acceptable will lead to harm), until the situation sees you powerless to be a giver. In that case, it's super harmful, because you'll feel like you're wrong and you won't be able to change it.
Second, we ask "where does thi control theory come from?" Aka, why do I feel and act like this. What led me to place such a condition on my acceptability as a person? Once you find this answer, you're realizing that feeling inadequate is your root problem, that the need to offer compassion is the solution your brain came up with, and the reason why your brain came up with that solution will probvide info about the nature of this feeling of inadequateness. In turn, this will give you something to work with in point 2)
Ok, I realize this is a super long post, and that I may come off like I'm making assumptions about you. In that case, I apologize, but I've been in this situation too, and want to provide you with as much info as I can, because info=tools to solve stuff, even if that makes me look rather arrogant, or a bit of an asshole.