Crap, this sounds like it could be columnaris. It's also known as mouth rot and mouth fungus but is actually bacterial. It's often caused by poor water quality and/or stress, so if you've had a 'bit of a fish kill' (what happened?) I wouldn't be surprised if it is columnaris. It could be a total overreaction, but given the fish's behavior and the history of a tank crash, it's better safe than sorry IMO.
There are several different strains of columnaris. They respond to antibiotics. Tetracycline is most commonly used, but you can use oxytetracycline, kanamycin/streptomycin/erythromycin etc, chloramphenicol, or just about anything marketed as an antibiotic. If you can't get antibiotics - in some countries you can only get them through a vet and it's really pricey - people have attacked columnaris with various substances in desperation, with differing degrees of success. Most medications marketed as antibacterial do something, but don't bother with Melafix, it isn't strong enough. Anti internal bacteria by Interpet knocks it around a bit. The jury's still out on whether temperature changes do anything. I've cured a platy of columnaris by using salt - 30 minute seawater dips four times daily, then returning the fish to weak brackish (2tsp salt/gal).
Isolate the fish - a 2 or 3 gallon plastic container is fine if you don't have a designated hospital tank. 5 gallons is ideal as lot of meds are 'add one tablet/x mL per 5 gallons. Get a cheap plastic plant for the fish to hide in, and add ammo-lock to the water if you can get it (otherwise you will have to do water changes while medicating, which is a pain in the you know what.)
Then up it with whatever medication you can get your hands on. With the weaker strains of columnaris, it's really a case of bothering it until it goes away. With the stronger ones... well, I've had one go through my bettas that kills in 18 hours. There was nothing I could do except watch them die. By the time the symptoms appear, it's too late to treat, because the fish is dead before the antibiotics can kill the bacteria. In the end I euthanised every fish that had been exposed to it (contaminated equipment), bleached everything. Lost a huge amount of breeding stock.. that was awful. It probably won't happen to you in a community tank, but I still think you should get the infected fish out ASAP.
If you dont' have any meds, don't panic. My LFS had a strain of columnaris a few weeks ago that was caused by stress and ammonia exposure of new stock in transit. It started on the mouth, as a few white spots, and then spread, and the mouth appeared to fray. They caught it before it progressed too far, added salt to the water, and didn't lose a single fish. The really, really bad strain I had began as a fuzz all over the body and isolated finrot. The true 'mouth rot' strain is one of the least virulent. If you have any salt that doesn't have iodine in it (often sold as cooking salt or rock salt) add 2 teaspoons of it to each gallon of water in the hospital tank. A guppy is capable of tolerating quite a lot of salt compared to most tropical species, so this won't hurt it at all. If you can't get a stronger medication, make up another container (1 gal is fine) and quadruple the quantity of salt, and put the fish in this solution for half an hour four or five times a day. Watch the fish while it's in there (or at least check on it frequently) - get it out if it gasps for breath. Make sure you acclimate temperature when moving it.
Sorry about the excessively long post... I've had a lot more experience than I'd like with this particular disease, and if I had to obtain the knowledge in such an unpleasant way, I do try to stop other people having the same disaster.
forgot to mention... whatever you do, DO NOT put antibiotics in your whole tank... it will kill your cycle.