Have you ever tried briefs instead of the boxer type of underwear? Briefs would tend to hold your penis in a comfortable position without movement as with boxers.
At your age, you'll experience different sensations and pains in your genital areas depending on clothing, soaps, lotions, and your normal cycles. Hormones are going to make some of these more intense. Seems you're beginning to see that now. Maybe briefs for a bit, or maybe just a bit of moisturizing lotion on the tip in the morning. Good luck!
It may be the type of underwear. Especially if you are exercising or doing some sort of strenuous movement and it could rub wrong.