I was in Texas from January 2016 until 06/2016 prior to moving to NYC and working in NJ

In the Personal Info section, you'll enter that you live in NY, and that before that you lived in TX, and you'll enter the date that you moved. You will also indicate that you made money in another state (NJ).

Enter your Texas wages and all your other wages  in the Federal taxes section, under W-2s. You'll be preparing a Part-Year Resident return for NY, and a Nonresident return for NJ. 

First prepare your NJ return. The numbers will transfer over from the information that you entered in the Federal sections, and you can make adjustments to show how much of your income came from NJ.

Next, your NY return will be similar. You will reach a screen Tell us about your New York resident income where you can input how much of your W-2 wages was from the time that you were a NY resident. See the screenshot below. Proceed all the way through both returns.