I keep a glass on the sink that I use to drink from during the day, so it
gets washed every couple of days. I use this glass to top-up my cat's water
bowl.  Is this a health risk for my cat?  I'm wondering if there is a
chance of transferring something from me to her.

The reason I ask is that she has watery eyes.  It doesn't seem to bother her
too much (and her nose is dry) so I assume she's healthy.  Sometimes her
eyes are fine, othertimes they're a bit watery.

Thanks for any advice.