State filing with 2 different states

Yes, but TurboTax will take care of that.   Make sure you add NY in the Other State Income box in the personal information section.   When you tell TurboTax you are a resident of PA but did earn income in NY, we will prepare a NY nonresident return.    When you do your state taxes, prepare the NY return first so that TurboTax can make sure you get credit on your resident return for taxes paid elsewhere.   How do I file a nonresident return?   Use this help article to make sure your personal information section is set up properly.

Your resident state will tax all of your income but will give credit for taxes paid to another state.