Stretch marks are super-common during the teenage years, when the body is growing a lot. Lots of girls have them, but they tend to show up more on some skins rather than others. Often they go away with time. But obviously you're concerned with right now! In terms of Prom or Homecoming, I think it's a better idea not to look to your dress to do the job of covering your arms, shoulders, and back. The dresses that do so can be pretty horrid, and in limited supply as well.
Instead, I think it's better to find a great dress that's too bare and then find a cute cotton or cashmere sweater, a lace or velvet jacket, or something of that nature to wear over your dress to cover your arms, back, and shoulders. You can also try a real or faux fur stole that hooks in front so that you don't have to hold it, or a crocheted openwork sweater. The fall and holiday season are the best times to find a cover-up that will work with a fancy dress. An alternative is to have a lace or other fabric jacket made in a color to coordinate with your dress.