Oh no! I can tell you from experience that cat bites are very serious! Please urge her ot get a tetanus shot and it looked at by a doctor - she might need intraveneous antibiotics.

As for introductions - letting them sniff at each other under the door will help them acclimate to the smell of each other. LEt them play footsies under the door. It might take a few weeks, it might take a few months, but it usually does eventually work. There is the rare occaion where one or both kitties just refuse to like the other.