There are two components to your question: 1- do you need a license to be a make-up artist and hair stylist; and 2 - do you need an LLC. I do not know offhand whether a make-up artist or hair styist needs to be licensed, but you can check with the New Jersey State Board of Cosmetology and Hairstyling.
Regarding the LLC, if you are starting a business venture, it is normally prudent to create an entity that provides you with legal protection and possibly favorable tax treatment. LLC's are good vehicles to provide you with liability protection while no subjecting you to the double tax that you would incur if you created a corporation.
If you want to discuss further, I'd be happy to speak with you. (908)233-6800.
Please be advised that my response is for informational purposes only based on the limited information you have provided. You should not construe such it as legal advice, and should consult with an attorney for advice on your specific legal issues. My response does not create an attorney client relationship. You should not act upon my response without seeking advice from a lawyer.