I've got a "thing" with public pools

Well now that my baby is well...no longer a baby, she's started to do things that don't really invovle me: preschool, playing at the park and swimming lessons. Now to be honest I'm so glad that swimming lessons don't require parent participation because may I just say that public pools are disgusting...yeah I'm sure there is lots of pee in the pool and all those people that create human stew in the jacuzzi, but for me that's not the worst of it...oh no far from it, for me the most vile part of the public pool is the floor...it's everywhere, it's unavoidable and it is gross. I cringe when other people put their bare feet on this floor, the half wet, kind of muddy, with the occasional clump of hair and why is there ALWAYS a used bandaid...for the love of all things holy why the bandaid??? This neurosis is all on me, I get it, it's my problem...but I am seriously struggling not to make it the littlies problem...it's already rubbing off on her. Is it such a bad thing to want to avoid other people's filth...I mean is it really?