You can ask the public school to evaluate him even though he is enrolled in private, but I'm not sure what the evaluations generally consist of in this case (probably at least academic testing for a learning disability if you have any concerns about that). I do think some sort of eval would be a good idea at this point, even if you have to pay for it privately, to make sure you are not missing a disability.

Sorry things have not been going well. With a pregnancy, especially, that makes it really tough.