|My fish have sores on their bodies and mouths, I suspect this is a bacterial infection but I don't even know where to start with treatments.
The short read is that you MUST establish that water quality is "perfect" via water testing, and THEN you need to layer at least two different antimicrobials on the fish without causing undue strain.
A pair of good medicines together is potassium permanganate on a four day interval and some medicated food. Better still would be injections of antibiotics and medicated food. Control of Flukes could be rapidly handled with SupaVerm. There's an article on how to use it over at KoiVet.com
At the first signs of disease, I recommend an immediate assessment of the fishes' environment. As part of their natural biology, all fish excrete Ammonia (So, test for Ammonia) -
Ammonia is converted into toxic Nitrites. SO, RUN A TEST FOR NITRITES.
Finally, pH is a measurement of Hydrogen ions in the water and needs to be read at a level above seven-point-zero for Koi and Goldfish to be happy. RUN A TEST FOR pH.
To control Ulcer Disease and body sores, you need to accomplish the following
(1) Reduce crowding
(2) Provide "perfect" water quality
(3) Eliminate all parasites from the fish. Assume your fish have Flukes when Ulcer Disease is playing havoc on the collection.
(4) Get the fish to eat.
(5) If possible, warm the specimens to 74-78 degrees but do this slowly or you may kill them.
(6) Make sure the fish have cover in the quarantine. They will be highly stressed, and only get worse, if they cannot hide.
(7) Potassium permanganate and hydrogen peroxide will become very important in the environmental clearance of flukes and the peroxide will remove the potassium's brown residue later. See notes on Potassium in the treatments (Look it up!) section and the article on Peroxide.
(8) Injections will be the only way to save the bacterially infected fish that will not eat. Soaking him in a bath of antibiotics is a last resort, but will not save valuable fish lives.
I strenuously recommend that you obtain the necessary injectible antibiotics and the syringes and needles, and commence injections immediately.