I'm sure you mean well as you are here on a cat site asking for advice, however you are doing your cat an injustice by not getting it adequate medical care. From the way you described the potential issue- it could be something that requires immediate medical examination and care by a lisenced vet. As an owner -it is your responsibility to get your pet medical care when it has been injured. If you neglect those duties as an owner- most places consider that animal neglect (i'm not accusing you of it- however i work for Animal Control in my area as a veterinarian technician -if someone here chooses not to get an injured animal medical care- it is considered abuse/neglect and they are charged appropriately for the violation.)
Please consider working out a payment plan with your vet- most of them will be more than willing to let you make a payment plan with them and allow you to pay over a period of time. You may also want to check out www.carecredit.com
as Jennifer has already suggested. They may be able to help you hon
In the mean time- please start keeping your kitties indoors. Allowing them to venture out unsupervised is NEVER ok. I can not tell you how many cats and dogs have wound up in the shelter where i work after "disappearing" from home, roaming for territory/mating/food, getting attacked by other animals, attacking other people and being held on rabies watches..the list goes on. By allowing your cats to venture outside and thus venturing the chance they might come in contact with other cats/dogs- you greatly increase their risk of getting in a fight over territory/ other factors and as a result your beloved pet might be injured badly (as it seems to be at the moment), develop a disease/virus as a result of exposure to other infected animals, be hit by a car, shot at by neighbors, you name it.
The safest place for a pet is indoors. If you would like to let your sweet kitties get a little fresh air every now and then- please consider buying a cat safe harness and leash so that they can still go outside for walks and fresh air- but will not run the risk of being injured, killed, or infected with serious conditions as they would be when allowed to roam. It's easier than it sounds to get a cat to walk on a harness/lead!
All of mine go out in the garden on theirs and they love it- they get to get fresh air, and i have the peace of mind that they are safe with me as i'm there to supervise. It's the best of both worlds.
If you own your own home- you might also want to consider building a cat safe enclosure in your backyard- that way your kitty can get fresh air/enjoy the outdoors without being allowed to roam. If you do this though you must always keep in mind that they are not fool proof and there have been instances of other animals (raccoons/etc) breaking into enclosures around my area and when that happens the potential for other animals to do them harm if the enclsure isn't properly secured/build is always there. Supervision is key to a healthy/safe pet!
Always make sure your pet is up to date on all vaccinations as well as their rabies vaccine.
Now onto the medical issue at hand- the swelling could be the result of a number of medical problems- broken bone, an absess, you name it- without having him here to personally examine him, i would be unable to offer medical advice to you. Therefore my best advice is for you to take him to a vet and see if they will work out a payment plan with you. Most of them will be more than willing to! Just ask!
If he does indeed have an absess or the joint is physically ripped open due to a tear/fight- one thing i've found to work incredably well is mixing table sugar (white refined like you'd use in coffee) with betadine antiseptic solution. You mix the betadine and sugar together till it forms a paste and then you take gauze and soak it in there- you use the gauze to gently clean the infection site and then use another clean, freshly dipped gauze and then apply stretch wrap over it to hold it in place and change it daily. If it is at the "armpit" area- the infection site must be shaved properly and wrapped appropriately so that the wrap and gauze stays in place otherwise you will do more harm than good. If you don't know what you're doing or how to wrap the site- it is best to let your vet show you how to properly care for it. Please do not apply any solutions/etc to this cat without first having him assessed by a vet to make sure another course of treatment isn't necessary instead.