I do a lot of intense workouts and I sweat a lot so what I usually do is put a tank top under my t-shirt. My fav's are the under armour ribbed tank tops - they are perfect, just a suggestion if you are self conscious about it.
No one sweats at my gym either. I go to my University gym, and all the girls have make up on and look like they could just walk off the treadmill and go for a date afterwards.. Maybe its because they are practically naked while working out? I really have no idea lol