First, if anyone is heading off to google, you will do better looking up WARBLE fly or warbles, not botfly (I believe it is in the same family as 'regular' botflies, but many other bots have larval stages in the intestinal tract - "warble" will cut you right to the chase on the relevant critters).
You should not mess with a warble wound - best to leave it alone, or see a vet - because trying to cut or squeeze the larva out of its disgusting little home can kill or 'pop' the larva and lead to the animal (i.e. Fluffy or Bossie or whomever) dying of anaphylactic shock.
HOWEVER it doesn't really look like a warble to me and a quick google supports my inability to ever recall them being said to affect *birds*. (I'm not guaranteeing this is an absolute fact, but all in all I think a warble is not the most likely thing.
Yes, humans can get warbles, but only from the adult warble fly laying its eggs on a break in your skin, NOT from touching a warble that's livin' in another critter.
Staph infections OTOH are highly contagious and one of the prime reasons you should always wash the HECK outta your hands after any time that you deal with an animal's infected wound.
Good luck,
Pat