Hello, my name is***** and I have over 20 years of experience as a veterinarian. I understand that your little one has a bad tooth with obvious outside swelling. She likely needs that tooth extracted and the rest of her teeth thoroughly cleaned.
I understand that your regular veterinarian is beyond your means financially now. It also sounds like she is well beyond brushing at this point.
Your other option is to contact your local shelter or humane society and see if they run a low cost clinic or know of one in your area. If not here is a web-page that lists some that may be able to help: http://www.humanesociety.org/animals/resources/tips/trouble_affording_pet.html?credit=web_id91754962#Assistance_by_state
Other sources of help can be found here: http://speakingforspot.com/?p=Financial%20Assistance%20for%20Veterinary%20Care
It may take a while to find a source of help for your girl, so perhaps having her seen at the local shelter clinic and getting her on antibiotics now will help at least keep the infection down in the meantime.
It may be helpful too to use an oral rinse with Chlorhexidene such as CET rinse to help control mouth bacteria. Here is a link to show you the product: http://www.1800petmeds.com/C.+E.+T.+0.12%25+Chlorhexidine+Rinse-prod10592.html
If she is eating and drinking normally and has no history of bleeding tendencies or a sensitive stomach you can give her buffered aspirin at home for a couple days. Buffered aspirin is the only over the counter anti-inflammatory that can be used in dogs. Aspirin does cause stomach and intestinal irritation and ulceration as well as clotting problems so should not be given for more than 2 to 3 days consecutively and should always be given with a meal. It should not be given the week before any surgery or dental procedures. If you choose to use it watch for lack of appetite, vomiting, blood in the stools or dark tarry stools and stop immediately if you see those. Do not use aspirin if your dog has liver or kidney disease or a history of a sensitive stomach or clotting problems.
The dose for aspirin is 5mg to 10mg per pound of body weight orally every 12 hours (about one low dose 81mg aspirin for a 12.8 pound dog every 12 hours). Always give with a meal. Do not use for more than 2 or 3 days.
You can also apply a cool compress to the swollen areas to reduce pain and inflammation.
Best of luck with your pup, please let me know if you have any further questions.