"Yes I made money in the previous state I lived in"
In that case, on the part-year resident return for the previous state, enter ALL the income you earned there for the entire tax year including the portion that you earned after the move. Answer No to the question about having "other state income". Then on the part-year resident return for the new state, enter all your income earned after the move.
Complete your previous state return before you do the new state return, so that the new state will credit you for the tax paid to the old state on the portion of your income taxed by both.
The "other state income" question is looking for income earned in a non-resident state. All your income was earned in a part-year resident state.
As far as I know, New Jersey is the only state that requires the taxpayer to file both a non-resident and a part-year resident return in your situation.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
