Mildly Infuriating

So I was a fool, neighbors dogs got into a fight, not abnormal, but never had it been more than a growl and a nip and the dogs know oops they aren't playing, stop. Well the larger dog has been sick, (princess). So when playing the smaller dog apparently (new to the family ~6 months, maybe 3 years old) saw it as an opportunity apparently. When playing (German shepherd next door to them on the other side, so they run and play with a 4' fence between them. The shepherd can jump the fence if he wants, but doesn't except few occasions whole bored. (He came to visit me on Oct. 31 while I sat outside, put him back, jumped over and came back to hang out). I have no issues with the shepherd as he gets aroundy chickens, and does not hurt them. Today my neighbor heard his dogs fighting and tried to break them up. He tried putting a rope around princesses neck to pull them apart, but the smaller dog had her by the underside of the throat and would not let go. I heard it from next door and ran over. There had never been blood spilt before In their playing, but there was blood clearly now from biting around the throat and I couldn't tell who. I assume princess. He was throwing a 5 gallon bucket of water (near 30F 0C here) at the dogs to see if they would sperate. I hopped the fence and took the smaller dog who had the latched jaw by the scruff and pulled her off. Then got him to take princess to another small gated area. The smaller dog was fine with me, but when she realized playtime was over (tail wagging, madman of a young lady) she grabbed my forearm, I told her no, and pushed her off and she immediately stopped. (Yes she's dangerous and I was dumb). But her entire canine tooth went through my forearm and I had a hole near a centimeter round.). My fiance doesn't do well with wounds. She immediately started telling me I need to go to the emergency room, but honestly I'm poor, and I wasn't bleeding much at all. (I'm stubborn yes, but she missed anything important, I mean not bleeding like... 1/60 of a ketchup packet and no bandages.). Pure luck. So I cleaned it with cold water doused it on hydrogen peroxide and made sure it was covered. But now my fiance keeps acting like she's the victim, and it's an act of me against her. It's been near 10 hours, I have full feeling in the hand, no puss or heat, nothing other than mild swelling. I traced it with a pen just to make sure the bruise doesn't expand and I don't know. But Im just tired of getting told I don't care about her, because I won't spend money we don't have to make sure I'm okay when I got bit.

Edit: also I should say he's a great neighbor, he will come feed the chickens and give them attention for fun, if he has nothing to do , he will mow our lawn and help out with ever being asked. So ~300 worth of medical assistance, though he offered, I'd never allow him to pay. I've never asked him for anything, but he has been helpful for more than 4 years I've lived here. If anything I would swear I owe him money for his hospitality