Also, I have to amend my return to correct my dependency status question. My mom said she has my name on her return because I still live at home and was attending school full time however, she cannot claim me of course because of my age (26) and my income for 2019 (9,336). I just realized I mistakenly clicked someone can claim me but my returns were accepted. Will the IRS correct that readjust the calculations and send me a notice?
For the federal return, at your income level, it will make absolutely no difference if you indicated you were a dependent or not so don't both amending a return that will not change. As for the stimulus payment ... it is too late to get it now so you will apply for it on the 2020 return you will file next year ... just make sure you don't make the same error again in the MY INFO tab.
For the state returns ... you will have to file both a NY non resident and NJ resident return and you should get a credit on the NJ return for the NY taxes you pay and they may also add a credit ... review both returns carefully to see what the NJ refund consists of.