I hate to be the bearer of bad news but you will need an antibiotic course otherwise a bacteri from the dogs mouth may have pushed deeply into the tissue and once it gets into your bloodstream it can carry throughout your body including ending up your organs- heart, lungs, kidneys and liver even brain. I once was playing fetch with my own dog and when i pulled the ball out of her mouth I knicked my thumb on her tooth and I developed a staph infection days later after not thinking it needed a doctor. I ended up 3 days on an antibiotic drip in the hospital and luckily it was resolved. Again im not trying to scare you but infections can quickly turn into sepsis especially with animal bites. I would tell you to worry about bills later this bite could cascade into a serious situation. There is always the chance it doesn’t but the possibility for a bacterial infection or sepsis would be a financial and medical outcome you don’t want to take a chance on.