Well, we went to the vet today (hope I'm not hijacking nubus's thread). He said Daisy had a bacterial infection on her lips and he gave me some antibiotic cream.
After all the posts about plastic bowls, I thought about it and I thought "well, our bowls are ceramic (food) and stainless (water), so we're ok there." BUT, then it occurred to me later that when we have Daisy crated during the day, we have a bowl that's made to clip onto the wire crate. She loves drinking out of this bowl, even if she's not crated, if there's water in there, 9 times out of 10, she'll go in her crate and drink out of it. And it's PLASTIC. Duh. So I went out and tried to buy a stainless clip-on bowl. No luck. So I put a small stoneware hamster food bowl inside the plastic bowl, so she will be drinking the water from it, but it still has the clip-on feature I like for in her crate. I will look online for a stainless clip on bowl so it will hold more water. I'm sure they are out there somewhere. Everything is, right?
He also said I could take a Stridex pad and rub it on her lips once a day in addition to the antibiotic cream. (I don't know if Stridex is international or not -- it is an acne cleanser/astringent for humans.)
So hopefully between the different bowl and the medication, it will be cleared up soon.