Summarize:

If you haven't worked up a major sweat, a disinfectant wipe may be sufficient to clean yourself. Some schools are even handing these out to students in gym class instead of showering. Just bring a pack in your gym bag and wipe down your armpits and other smelly areas. If you're self-conscious about this, you can wipe yourself down in a bathroom stall. Stop at your locker to pick up a towel. You can secure the towel around your waist and then slip out of your pants. Remove your shirt next and quickly slide the towel up under your armpits if you want to cover your chest. You can bring your towel into a bathroom stall and change out of your clothes in the stall. Then emerge already wearing the towel and no one will have seen you change. If you're going to a neighborhood gym, try not to go during peak hours. During lunch or right after work, there's bound to be tons of people at the gym, and so it's more likely the locker room (and showers) will be crowded. Ask a trainer or the person at the desk when the gym is least crowded, then try to fit your work out in during those hours.  If you're in gym class and trying to avoid showering with your classmates, talk to your teacher and ask if you may shower after everyone else has done so. You can also try to wait the other students out, taking your time so that most other people are finished showering by the time you are ready. If your school insists on students showering after gym class, talk to a school administrator and see if you can take gym during final period. It will be much easier to talk your teacher or coach into letting you skip the shower if you assure him or her that you're going to rinse off when you get home. Part of the reason your school wants you to shower is that if students don't clean off after exercising, they may spread serious diseases like MRSA. If you're going straight home after gym, however, the chances of that are slim. If you are experiencing bullying or terrible anxiety because you have to shower at school, ask your parents to write a note to your teacher. You may have to meet with your gym teacher or a guidance counselor, with or without your parents, but if the situation is severe, you may be excused.
Use disinfectant wipes instead of showering. Wear a towel to and from the shower. Try to shower when very few people are around. Rearrange your schedule if you're a student, making gym your last class of the day. Get a letter from your parents if you can't get comfortable.