I would have been worried like you were also. I know we have to take our furbabies to the vets. But I've often wondered the same thing. About how many pets were in the same waiting area as us during the day and were any of them contagious.
We were at the vets once and this couple had their cat in a cage and their little daughter was wondering all over the waiting room, touching her cat in the cage, hands on everything and she came over to try and pet Rudy. I said something like, "I'm sorry but I really don't know why your kitty is in here and I'd rather you not pet Rudy. " The parents didn't say anything and my husband just looked at me.
I'd rather be safe than sorry.
I'm sure your little one will be fine.