My suggestion to you would be this: Overcome your shyness.
Like you, I have beautifully oversized genitals. Like you, they show in pants. Unlike you, I don't care that people stare.
I have used the bulging pants to my advantage several times.
1.) As a college tennis player, I enhanced their size with the use of a cock ring. Because we had to wear the tight short shorts for tennis that were standard back in the 1980s, I had a prominent bulge that caught the attention of, and, intimidated my opponents on the court.
2.) During meetings, I would enter meetings with a big bulge in my pants, enhanced by a cockring to make it all look even bigger. Whether people want to admit it or not, a big dick is an unspoken instrument of power. People defer to it. By letting others see it without being obvious about it, people knew that I "walked softly, and, carried a big stick".
3,) In lines at airports I have found that the gatekeepers are frequently women or gay men. By showing a bulge, I have received much better and faster service than I would have received by concealing it.
4.) Invest in a speedo in a nice color, such as royal blue or poppy red. They have more than paid for themselves in free drinks from horny, lonely travellers many times over.
Good Luck to you!