What you are describing sounds like it could be impacted and infected anal sac(s). This could certainly lead to discomfort and swelling, both of which quite often lead to "scooting".
The anal sacs (or anal glands) are little glands located at the 4 o'clock and 8 o'clock position if you are standing behind your cat. They are normally about the size of a green pea in a cat. They have a little tube leading from the anal sac to the anal opening, and what Mother Nature intended was that every time your cat defecates, a few drops of the fluid contained in these sacs gets deposited on the feces.
Sometimes, however, the little tube gets blocked and the anal sac cannot empty. This can happen if the stools are smaller and thus are not squeezing the anal sacs as they go by. Anal sac fluid is continuously produced by the body so the sac gets more and more full. Eventually it can rupture out through the skin.
Given how close the area is to fecal matter, anal sac ruptures seem to always get infected.
Treatment requires oral antibiotics since the sac is under the skin and the only way to get the antibiotics to it is by the blood stream, which means we have to give the antibiotics by mouth.
When I see patients with an anal sac abscess, I generally clean the area, start them on antibiotics and then see them back in a few days (once some of the swelling and pain have gone away) and try to express the anal gland to get rid of the blockage in the tube.
Often I have to see the patient a few times. Also, I like to see them a week or so after the antibiotics are finished to make sure the blockage (impaction) hasn't returned.
Here are some links to further information:
In terms of what you can do to help today, the most helpful thing would be for you to apply a warm compress to the area. If you have antibacterial soap in the house (Hibitane or chlorhexidene soap would be ideal, hand soap would be ok for now) you can add about a tablespoon to a cup of warm water. Put a washcloth in, then wring it out. Hold the warm, damp wash cloth to the swollen area for 10 minutes, re-warming it every 2 minutes or so. Wipe the area with a plain wet washcloth and pat dry.
This may help to remove any little plug at the end of the duct and thus allow the anal sacs to empty.
here are some videos that explain more about anal glands:
I also want to mention that there are NO human pain killers or fever reducers that you would have at home that are safe to give a cat. Aspirin, acetaminophen and ibuprofen are all very toxic to cats and should never be given! You can read more about them here:
I do think your cat is likely going to need to see her veterinarian to get some antibiotics to treat this. However, if your vet is not open at the moment, then the suggestions above may help to keep her comfortable until your vet opens!
I hope that helps you.
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The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would strongly advise contacting your regular veterinarian.