What happens if you tear your vaginal opening and it bleeds during first time sex? Is that bad or will it get infected?

Common to have tear. Very common to have a tear with some bleeding during first or even subsequent sex. Have partner be gentle, go slowly, and consider the use of KY jelly - to help with an easier insertion. Agree with the previous doctor - infection unlikely.
Common, not bad. It is very rare to get an infection from tearing of the hymen when you first have sex. It is possible, but hardly ever happens. You could of course get an infection like chlamydia or gonorrhea if your partner is infected, but that could happen anytime.