Yeah, I can personally reccommend Driclor. I tend to have really clammy/sweaty palms - nowhere else, just on my hands (weirdass genetics, thanks dad). I did try it on my underarms too a while back (because I thought it would be fun if I could get through a PE lesson and not sweat), so I can say it stings like a bastard if you've shaved recently: it's very much alcohol-based.
You apply it last thing at night, at first every night but then you can slacken off to once or twice a week, two weeks, etc and eventually you don't need to use it much at all. It's a bit weird when you wash it off in the morning, as it seems to 'absorb' soap for a bit, but it's really fine.
Good luck! (oh, and just a note, it might not be behind the counter... it was for a few years but recently I spotted it near the deodorants section in Boots and Superdrug).