First factor - you can keep on as much or as little as you want when getting a massage. Most people are more comfortable with less clothing, but there is nothing wrong with just taking your shoes and belt off.
In most states in the USA, a massage therapist is legally required to provide adequate draping. This means you would be covered with a sheet or a towel and only the area being worked on is usually uncovered.
Nothing that would be kept covered at a typical family beach should ever be uncovered (think bikini). If you want more coverage, it is your right to request it and end the session if you are not listened to.
If you want to keep on underwear, a bathing suit, or even a pair of running shorts and maybe tank-top, I have had some clients routinely keep on that much or more, and I just work with, through, or around the clothing.
If you don't want an area touched or worked on, feel free to say so. Some love glut or ab work, some can't stand giving or receiving massage on the gluts and abs.
Other question - does the therapist know that you're 15? If you were my client, I would want at least one of your parents within earshot, if not in the room at your age. For your protection and for mine.