Katt Kittz meow
yes this happened to me not to long ago, my cat attacked me and bit through the bottom and top aswell as you i am allergic to cats and it got swollen for a couple of days, for me i just put peroxide and a bandade and it webt away in a couple of days, but the bite left marrks for quite a while.. Maybe you should go chek if you are allergic as well you never know.
Clean the wound
You should clean the wound no matter how small the cut to the skin. There are many bacteria (germs) in animal mouths. Cleaning will reduce the chance of infection. If the wound is small, you can clean it yourself. Just use ordinary tap water. (There is concern that antiseptics may damage skin tissue and delay healing.) Wounds that are large, deep, or dirty are best cleaned by a nurse or doctor. After cleaning, cover the wound with a sterile, non-sticky dressing.
Consider going to hospital or seeing a doctorWound care
If part of the wound has dead or damaged skin then it may need to be 'trimmed' or removed. This is because dead skin is ideal for infection to develop. Gaping wounds may need to be stitched, glued, or pulled together with sticky tape. Open cuts to the face or head will usually be closed as soon as possible. For cuts to other parts of the body, sometimes a doctor may advise to wait for a few days before closing the wound, particularly if the wound is more than six hours old. This is to make sure the wound is not infected before closing it up.