Suggestion for you (I recently went through a bought of cellulitis with my youngest and this is what we did per doctor's instructions):
Get some Epsom Salts - dissolve about 1 teaspoon in one cup of warm water (as warm/hot as you can stand). Take gauze pads, saturate them in this solution, place on your thumb and leave there for at least 15 minutes - do this twice a day. After you have done the soak, take some betadine (the red medicine - can be found at Wal-Mart - they have their own brand that is cheaper) and "paint" the area with a q-tip. The betadine will help speed the healing of the wound along with the epsom salt soaks.
If at ANY time you notice redness around the area that grows, gets hard, or red streaks start up your hand, get to a doctor IMMEDIATELY! That is an infection and the only way to get rid of it is antibiotics.
Good luck and keep us posted on how you're doing
