Michelle - Welcome to the Forum.
Generally, asking for legal advice on the internet is not the best possible cource of action.
In many states, it is perfectly legal for one person, of age, to sell another person, of age, a firearm face to face without any paperwork and without any background check.
HOWEVER - I would HIGHLY suggest that you contact your local authorities for the rules and regs in YOUR area.
The police are not going to tap your phone and place an unmarked unit to follow you because you ask a legitimate question about the law in your area. Well, unless you live in NY or Kalifornia.