I think he has every reason to be afraid and experience such stress at a doctors visit, especially if he does not have language yet. If you are sure that these are two issues, then I would just speak to your doctor and see if you can find a nuetral site (like the parking lot) for doctor visists until his anxiety and stress is lower. You might try to make some fake appointments where he has a pleasant expierience, if your doctor will cooperate.
Also, I would invest in a speech and langague evlautaion. If you do not think he can understand the langague especially, I would go sooner rather than later. By age two he should have between 50 and 100 words and be putting two of them together into a simple sentence. You really want to get the earliest intervention you can. He may qualify for home services through your states ECI program, but also invest in private evaluations to supplement what the state may provide.
If you think that these two issues are related, that he has more stress or anxiety than is just caused by his doctor experience, then I would suggest that you call a Developmental Pediatrician. Since he has had an eye issue too, you may just want to go for a more indepth evaluation anyway, even if you are pretty sure that he is reacting to his bad experience with doctors with this behavior. It is pretty big behavior, but understandable, and I would just be really sure that you are not dealing with anything more global.
Good luck, I hope he gets over it soon. Poor baby!
M.