Scared of rabies

So I'm seventeen in Texas and about two days ago, my dad took our three small and vaccinated dogs outside to the backyard. There was a grounded and non-aggressive bat, which I'm told is a sign of rabies. He says they were close enough to sniff it but he saw it before them and kept them away, I haven't noticed any wounds on them. However, one of them got saliva in my mouth a few hours after seeing the bat and I haven't been able to get over the fact that I might have rabies. My parents aren't worried, I asked them to get me a shot but they said no. I can't just go and see a doctor as I don't have my driver's license. I've been looking up everything that could relate to the exact case I was in on Reddit and Quora and I keep getting conflicting information, sometimes I'll feel slightly better but then I'll feel even more confident I have rabies. I feel so scared and helpless right now, the CDC say rabies can spread through saliva getting into the mouth on their website. I don't know what to do or how to feel, it's driving me insane. I'm technically ban evading right now so I'm just looking for responses and I likely won't be able to answer. Please help, I don't know who to talk to and how.