You seem to have the motivation, the time, the money for a pedal across the US. It can be done for no more than you'd spend if you didn't go. (A good touring bike and quality gear can be sold at the end of the trip to recover about half the cost.)

At your age, a x-country ride is the equivalent of a degree in human relations, geography, logistics, and problem solving. It'll serve you the rest of your life.

Invest in the Adventure Cycling Association maps for their wealth of navigation info, points of interest, and free/low cost overnighting suggestions. You'll likely save their cost.

Go for it!