You say on the lateral side of your thighs which to me sounds like your IT Band. If it is then your IT Band is a facia band not a muscle which attaches at your hip and extends all the way down to your knee which if tight will pull the kneecap out to the side. The IT Band is hard to stretch but I stretch it with a foam roller and to the touch it is very very painful if tight and can be tender to the touch. Try doing some research on the internet and see if this is what is going on for you.
Jen
Hey, I'm a 21 year old female and I definitely have tenderness to pressure on both of my thighs: more laterally.... for instance, if I bump into something in that area, it takes a full minute for the pain to start decreasing. It's bothered me for a few years now, and I haven't gotten a medically professional opinion (i have light varicose veins in the area, as well, but neither my dermatologist or massage therapist had much to say about any of it). I haven't really experienced cellulite, per se, but I have been wondering if that's what it could be, because the skin feels more spongy to the touch in that area, and if pressed against, the slightly visible dimples become much more pronounced -- moreso than anywhere else on my legs.
However, my massage therapist mentioned that it could fluid build up -- but I don't know for sure. I wish I could tell you something that would help YOU! But I have to admit, not understanding this has been really disturbing me for awhile now, and even if it can't be fixed, I really need to figure out why it's SO TENDER. If you find anything out, please let me know, and I will do the same :)