You are fine! Everyone in NJ knows very well the undocumented population. I live in NJ and I applied to NJCU straight after high school. They didnt care I didnt have a s.s# didnt even question me or looked at me bad. They know it and they dont care. Stop being fearful. If you go to hudson ( assuming you're an A+ student) its a straight acceptance to NJCU and any NJ university.