You think the rest of the world is any different?
The US, the majority of Europe, a lot of Asia. They've all got high migration rates. And of course the population is always increasing. With that, there are going to be less properties and higher prices. That's how supply and demand works.
It's a problem that is never going to go away even if you try to stop migration into your country.
So you might as well stop complaining and adapt to the situation. Look for ways to solve the problem, find out how you can improve accommodation for people. Discover ways to make housing cheaper. Or take advantage of the inevitable and start investing in property.
But rather than blaming migration, I would blame your government. They need to start prioritising building housing. Most governments do. Sure migration doesn't help, but the governments are not doing what they should be to alleviate this. They bring more and more people into the country without building enough housing to keep them all here. The funny part is that I guarantee most of these politicians are landowners.
Do something other than wasting your time complaining on the internet. We all know migration is making it harder to find housing when it's already hard enough with our own population increasing. We all know that it's a global problem that is only going to rise unless we have Thanos do some population control.
The question is; what are you going to do about it?