I cycle to school and intend to wear my new Lycra shorts for my commute as they are much more comfortable. But I want to know if I will look dumb wearing the tight shorts, as my legs are only average and I'm only 15, and also if it will be weird stripping down to no underwear when I get changed in the locker room at school.
I'm currently a senior in high school, so I understand your concern about style. In my opinion, and that of all my friends, wearing lycra shorts to school looks ridiculous, no offense. I don't know how far your commute is, but when I take my road bike to school, it's only 3 miles, so I just wear regular shorts and bring another t-shirt I can throw on so I'm not all sweaty and throw a pair of sneakers into my bag so I'm not stuck wearing cleats all day. If you have a longer commute, just put a pair of basketball shorts on over your lycra shorts. It looks good, feels fine, and others can't even tell you have lycra shorts on underneath them. Baggy cycling shorts don't look much better than lycra when you're in high school, even just for your commute.
As far as changing in the locker room, that should be fine. I've done the same thing plenty of times. If you're self-conscious about it, you can always use a shower stall or something so you have some privacy.
Unless you are travelling really far (5+ miles) or going for some kind of home to school time trial record, just wear your regular clothes (tuck your trousers into your socks if need be) and cycle a little slower.
Too many people are too obsessed with racing their bikes places, but if you think of cycling as a faster and more efficient way of walking then you'll get on just fine.
Wear some non-Lycra shorts/tracksuit bottoms over the top of your Lycra ones if you are self conscious about them.
Change out of the Lycra ones in a toilet cubicle if you are concerned.
You can also buy baggy cycling specific shorts which have many of the advantages of Lycra based ones but without the concern about showing off your entire package.
A quick google for "baggy cycling shorts" found me loads of hits, top of which was this page from Wiggle a UK cycling shop.
For instance here are some possibilities:
Simply put, you shouldn't wearing cycling clothing to school unless your commute to school is really far.
When should you wear cycling clothing? When your destination is so far, that you can't do the trip comfortably in normal clothing. You should be aware that different saddles can also make a difference I have one for rides below 40km - this one is really comfortable.
I would suggest not wearing cycling shorts to school simply because you're going to wear them out much quicker as well as likely developing butt pimples.
The chamois in the shorts act like a sponge, a sweaty, greasy, bacteria filled sponge. Sweat will break down the elastic in your shorts, the longer you wait to wash them, the more likely they are to begin breaking down.
I commuted approx 9 miles a day to work via bike. I started wearing cycling shorts in the beginning then decided it wasn't worth it. I still wore shorts to work on hot days, non-cycling shorts, as I didn't want to wear them out. Purchased a cheap used bike with a seat that allowed me to ride without cycling specific shorts.
In the end, you certainly can wear your shorts to school, but most people don't have the same perspective as us cyclists and wouldn't understand the need for them, thus you'll probably get some remarks.
Rivendell has a lot of non-lycra clothes. Some of that stuff might pass for hipster.