I am about to go offline for the night, but wanted to leave you with some more information in case you come back while I am away.
Based on the description you have given, I am very suspicious that your cat has an abscess caused by a bite wound from another cat. Certainly, in 999 cats out of 1000 with that description, that is what I would find on physical examination! The bite would likely have happened 7-14 days ago.
Let me explain how this happens...
When a cat bite wound occurs, what happens is that there are 2 puncture holes - one caused by the upper and one by the lower canine tooth. The cat's teeth have a lot of bacteria on them, and these bacteria get placed deep below the skin when the bite occurs. The hole is small and quickly scabs over, leaving the bacteria below there.
The most common type of bacteria in the cat mouth is Pasteurella multocida - and it LOVES to grow in a warm, moist environment that has no oxygen present. And that is exactly what you have with a bite wound!
So, the bacteria multiply, and the body sends in white blood cells to fight the infection, and soon you have a big pocket of pus and bacteria: an abscess! The abscess grows bigger until it ruptures and the pus pours out. This relieves the pressure and allows the hole to close over which then allows the process to start again.
Bite wounds, ideally, should be treated with antibiotics within 24 hours of the bite. This prevents the bacteria from multiplying and forming an abscess in the first place.
Here is more information:
So, if any bite wound can be treated before it becomes an abscess it is so much less complicated (and expensive)! Getting the cat onto antibiotics right away should stop an abscess from forming. Once there is an abscess, she might need an anesthetic in order to lance and drain the infection, which makes it much more invasive and expensive.
Until you can get any bitten kitty in to see a vet (hopefully within 24 hours), 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) you can add a little 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, rewarming it every 2 minutes or so. Wipe the area with a plain wet washcloth and pat dry. The goal is to keep those puncture holes OPEN as Pasteurella bacteria don't like oxygen. If you let the holes scab over, then the bacteria will grow.
Given that your vet is not open until Monday, I would suggest that you apply warm compresses to this lump 3 times daily and try to soften/remove any scabs that you find on the skin as this will allow pus to drain out. Encourage your cat to eat and drink by giving canned food, and water from a can of tuna.
I do think your cat will need to see his veterinarian in order to have this lanced and to get started on a short course of antibiotics!
I hope that this helps you to help this kitty! If this has been helpful, please accept my answer.
If you need more information, just click on reply and I will be back in about 9 hours to provide it.
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.