Cat saliva bad?

This may sound a little odd, but I'm really curious.

So, I have severe eczema on my hands. They itch SOO bad at times, that I will either scratch the skin off or dunk them in scalding water in order to receive the itch.

My cat is VERY affectionate, and will sit on my lap and "groom" my arms, legs, cheek, etc. (Whatever is near her). So, I started giving her my hands to groom since her rough tongue is like the PERFECT scatcher that doesn't tear off my skin. She will sit there and lick all my itchy rashy spots on my hands and it's like a spa day for me.

Now, here comes the question... I have heard that cat have saliva that like...basically kills it's prey when they are bitten. Am I making my hands worse by letting her lick them?? It doesn't seem to be getting any worse, but I'm still a little worried ever since I found out...