Vet tech or vet?

Are there any veterinarians here? Basically I’m out of town visiting family and my cat end up getting fleas from moms cat and then he got tapeworm. My vet out of town told me to just give him something over the counter to treat it. That’s what I did. My question is my cat stays in my room and sleeps with me but he didn’t have bad fleas at all very mild. Could I catch these tapeworms??? I’m paranoid.