The reason your cat bite is getting infected like this, is because there is something like a poison in their salvia. I've heard they're one of worst bites to get. None, of my cats have never bit me that hard before, but I know sometimes their scratches get infected to...it's has something to do with some chemical they have...I'll have to do research. The alleve or some anti-inflammatory will be your best bet for this kind of pain because it will reduce the inflammation. Just remember to keep taking it, even when it doesn't hurt around the clock to kepp the imflammation down and keep the medicine in your bloodstream.. At least do this for the next three days. I would take 2 alleves every 12 hours. If you do that you'll see a significant reduction in the swelling and pain.

Also, another good way to clean it is to use witch hazel which is gentle but healing. I use that on all my wounds (including cat scratches) and it heals them really fast. Witch Hazel is really cheap. Too bad you aren't in PA becasue I make a really good wound healing astringent for my mom with witch hazel and calendula, chamoimile, and rosemary. If you want to know how PM me. Anyway, good luck. Just keep it clean and take your medicine