Antiperspirants block and clog up the pores in your body that produce sweat, they don't stop you from sweating in the first place. That sweat is still being made, and has to go SOMEwhere....
I used to sweat like a pig too. Someone told me to stop using antiperspirant deodorant, and let my body get used to having unclogged pores. Sure enough, about a week later of using just deodorant, I stopped sweating so much. Other than some sort of radical surgery, your body is going to produce sweat whether you want it to or not.
Also, for the record, I shave my pits, too. Even as a guy, I can't stand it when dudes lift their arms and this giant hairball pops out. If girls have to do it, I think guys should too ><