I am a resident doctor in PA and in my 2nd year. I am on J1 visa from India. Am I eligible for tax exemption? I f I have filed my taxes is it possible to correct them with the exemption, if applicable?

Every one on J1 visa is exempt form Social Security and Medicare taxes for two years. If you are considered a trainee, then you have treaty benefit for two years. You will file nonresident tax return, get personal exemption and standard deduction (as per treaty).

Read Your U.S. Tax Return: U.S. Tax Treaties for Students and Apprentices