You bet. I work for Animal Control in our area, so i can only really speak for my city's policy on things like that -but yes, if you went to your doctor and reported that you cat bit you- by law- your doctor is required to call the police dpt. and animal control to file a report. The animal will then be picked up by animal control and from there the injured owners are given two options.
Animal Control will hold them on a 10 day rabies quarentine watch at our location and charge the owner a boarding fee for each night, or you can board them at the vets office facility of your choice and pay their boarding fee. You can't transport them yourself though- AC has to.
The second option would be to have the animal put to sleep by Animal Control and we will then send off the body to the vets office to have the head decaptiated and then send the brain tissue off to Nashville (that's the city closest to us that does the testing) to test for rabies. So out of the two options, for your it sounds like your best would be the 10 day rabies quarentine and paying the boarding fees for it. You must prove that your pet is current on all vaccinations/rabies shots. If not you would be fined for that in our area. I'm sure most other cities work the same.
After the 10 day quarentine if the animal is found to be free of rabies symptoms- you will be summoned to court and have to appear before the judge to get your pet back depending on the situation, and you have to pay the boarding fees and any other fines before they'll turn the pet back over to you.
I'm sorry about your wound. I hope you feel better soon
I'm sure the kitty was just playing or it wasn't ment to be violent, unfortnately though- the rabies laws are required just as a safety precaution.