For wounds, I treat my animals like my children. Our method is washing the area with a 50/50 mix of filtered water and hydrogen peroxide every few hours (it may turn their fur a little orange until it grows out) and then smearing on an antibacterial zinc ointment/cream (like Bacitration - I've never had a bad reaction to bacitration, but like all things, watch closely for a bad or allergic reaction.) If you have Grapefruit-Seed-Extract (GrapeFruit Seed Extract) add about 10 drops to the water/peroxide rinse. Most important is keeping it clean and keeping them from getting dehydrated.
With bite wounds, outside of obvious infection, the main things are to check for internal or intracutaneous (under the skin) bleeding - if their gums start turning gray or white or they develop a large liquidy squishy lump under the skin, get to the vet *Immediately* to get the blood leak stop!
Also, if they get sluggish, dull-eyed, 'hot'ears, or slack skin that doesn't bounce back when gently pinched, they may be getting dehydrated. Serious dehydration can be helped by a vet giving intracutaneous fluids (saline solution, usually) - it is Lifesaving! Minor or early dehydration can be countered by making sure they drink at least 2 to 5 cc's of water per pound per hour - I use a 10cc oral syringe from the drugstore. If you have or can buy at a drugstore/grocery plain, generic, unflavored, unsweetened electrolyte solution (Like Pedialyte for babies/children) you can mix the filtered water and electrolyte solution 50/50 and give them that instead.
Cats, ferrets, small dogs and other small pets can dehydrated EXTREMELY fast, so keep a close eye for it.
Hope your little fighting tiger is better soon! =)