Hi. Even though your home is in NY, your residence is going to be NJ while you are in school there. After all, you will spend the vast majority of your time there, and all mail will be sent there. While you consider NY your home, and likely have intentions of moving back there after school ,your residence is considered NJ so you will technically need to get a NJ license. Sorry for the bad news (more DMN lines, sigh). Best of luck!
Just ask your local MVC agency or call them. Keep in mind that it is often cheaper for your parents if you are on their NY insurance and you are in NJ. Check with your insurance company. Trust me, I work in this field, I am familiar with many cases like your and you will likely gain on insurance rates if you switch. In addition, you can actually get a ticket for not changing over your license to NJ! PLEASE check this out, as i know many people who have gotten tickets for not switching over.