I've had similar issues myself. Currently on a mental health care plan and get 10 free sessions. Hopefully you find a psychologist that can help. The Dr can also prescribe anti depressants which are usually only about $6-7 a month.
I know moving to a different country and dealing with visas and finding work/friends can be tricky. Hopefully you'll get settled soon and don't worry about immigration finding out. We've already called about it and they said it wouldn't affect a visa application
All the best!!