Join the NRA and get their book on traveling with firearms.
As others have said, each state has their own laws. And you are responsible to obey them.
And make sure you have proof that you are the owner of the firearm. Even if you have a letter from a parent, as long as you are under 21.
"A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed."
Life Member NRA
Life Member NAHC