brionyclare213,
If you are indeed talking purely about other-state tax credits, it is not possible for a nonresident to get a credit for taxes paid to another state. Double check that you didn't inadvertently pick NY instead of NJ in your personal address information.
If you are just talking about bottom line refund versus tax owed, then, yes one could have your situation.
It's possible but not likely. You first prepare your NY return so that the tax credit for taxes paid to another state calculates on your NJ return. It is possible that you owe NY money if not enough tax was withheld, but they get the taxing priority for the income earned in that state.
New Jersey would likely only give you a refund if you had New Jersey tax paid in, and the amounts of credits, etc. bring your tax below the threshold of any taxes withheld. The only other possibility is qualifying for tax credits that are refundable in New Jersey. This scenario could happen if you had less income than last year, but it's hard to imagine you would have paid so much less tax to New York that you would have owed.
So, while we can't see your screen or account, it does sound like you want to review your entries. Maybe delete both states and start with the New York return first, just to be sure.