Does it look kind of like this at all?
http

/www.google.co.uk/imgres?q=platy+with+mouth+fungus&um=1&hl=en&biw=964&bih=539&tbm=isch&tbnid=0wa7Mov6xcMnDM:&imgrefurl=http

/www.aquariacentral.com/forums/showthread.php%3F174777-Has-my-fish-got-ich-and-cotton-mouth&docid=NWX0nd7wEX8PdM&imgurl=http

/www.swaffs.co.uk/images/2008/aquaspot/aquspot-0496.jpg&w=800&h=533&ei=ox7zTsS-IM638gPuvaDPAQ&zoom=1&iact=hc&vpx=127&vpy=167&dur=3847&hovh=183&hovw=275&tx=130&ty=55&sig=110957000062565089217&page=1&tbnh=163&tbnw=252&start=0&ndsp=6&ved=1t:429,r:0,s:0
Personally, i would get the fish out, using a cocktail stick i would carefully open its mouth to check it hasnt eaten something it shouldnt have...
I would tend to treat the tank, melafix is good if your fish doesnt have an obvious infection and i know people on this forum dont like medicating but tbh, its your choice, i think medicating is the safest way if you dont want it to spread... but you need to know what might be the problem first.
Especially as you have other unknown problems going on with another platy, i would err on the side of caution and treat (assumnig its not something stuck in the fishes mouth)
If i was treating, i would take carbon out and use a treatment with malachite/formalin and/or acriflavin in it. Myxazin uses all three, protozin will do the same job, anti fungal and bacterial treatment from Interpet or ESHA fungus and finrot.
Personally, i keep a big bottle Myxazin handy as its a really general treatment but works well for numerous problems.