You were in a public play place and your biggest worry is knowing that you held a child that had puked? Wash your hands and go home and change your clothes. You're not going to catch anything by holding a baby unless you lick your fingers after letting her suck on yours...and that didn't happen right?
Was it a little thoughtless? Yes? Is it something to be worried about? No. Unless you're living in a bubble, which you clearly aren't, she's been exposed to a multitude of germs.
My daughter will often cry until she pukes. The first thing on my mind isn't that she is sick...just to clean up the mess before the dogs try to eat it...lol. Ok ok, honestly, sometimes I let the dogs do most of the clean up.
Updated: Um, where did anyone say that you were a bad mom. Now you ARE being over-sensitive. You were ready to criticize your friend for being thoughtless. IF the kid was sick, you were alreadt exposed...licked fingers or not.