Your local public school should have information on testing, otherwise I would do some google searching.
As difficult as money may be I think you need him to see a specialist in education. There is a chance he could be gifted and this stuff is very boring. Or he may stress out easily and need to learn some methods to cope with the stress.
How old is your son, they don't like to test for dyslexia until about age 8 or 9.
I'm not sure about the laws where you are. In my state, if a child is in a private school, you contact the school district you reside in, and then they have so much time, once contacted, to evaluate the child and then decide if further testing is needed. There are a lot of other learning disabilities that it could be other than dyslexia. Good Luck
if you are German, don't worry education and medical treatment is free