First comment, never interfere in a cat fight. Second comment, if one erupts on your lap, make sure it’s not on a weekend, or after your doctor’s office hours. Amazing detail, notice after the noise and spray of fur is past, how your hand which was in the middle of said cat fight, is swelling up like a balloon. That isn’t from cat scratches or even cat bites (mine are too well-mannered to have bitten… this time) it’s from the incredibly powerful little-advertised cat kick. Consider the soft furry haunches, bunched with muscle. Consider the sinews, flexible and spring loaded. Now your hand looks like a pink softball. Ice is a very fine idea. However, examine first. What are the wounds that drip lovely carmine on your clothes and carpet? Punctures or slashes? Punctures mean go and see your doctor. Infection and Augmentin are likely shapes in your future. The faster you start your antibiotic the less your future discomfort. Perhaps more important, the less your possible future need of hand surgery. The hand is compartmentalized in its structure which means that all that bone and sinew work against great circulation and the flushing of toxins. It means that you can, if unlucky, get an infection in a tendon sheath. So if you have punctures, you have your marching orders from a fellow survivor. A tetanus booster is a splendid notion.
If not, I recommend letting the slash bleed very well, slather with povidone, dry, and use some butterfly bandages to pull the edges together. Watch that wound with skeptical care because even purely indoor cats carry quite sufficient biota on their lovely claws to cause a fine infection even of a nice open-type wound. Discretion is the better part of suffering.
This event happened in my home several years ago, and I escaped without a real scar in spite of all the drama. It’s useful to remember that when angry or afraid a cat’s eyes dilate and they become unable to focus. No cat in this condition can distinguish friend from foe which is why they will attack each other as well as the interfering human….