She will stop, just give it another month. My dd did that too. She had fuzzies galore in her little palms. And her hands did smell too because of the sweat. I pointed it out to her pediatrician and she said not to worry. Sure enough, a month later, she stopped. I think it is normal. I know there is information about clenched fists in several books I own, but I didn't think it applied to my dd. And it sounds like your dd is the exact same way.
The worst was bath time. She'd clench so hard that her hands would turn white (white knuckel effect) from clenching. I'd constantly have to open her hands.
Hang in there, it goes away with age.