botflies travel THROUGH the meat when they first hatch, and are tiny. they reside under the skin, (not in the meat) and cut a breathing hole . when they mature they are pretty damn big and nasty looking, like a giant maggot. they then squeeze out the breathing hole and drop to the ground, burrow in and hatch later on (turning into botflies).
i've only seen them in squirrells up here in NY, they are not in the meat so i never had a problem skinning the tree rat and letting someone else eat it.
i'm not sure what your deer had but i dont think its botflies...
wanna puke/ search "human botflies" on youtube. grossest stuff i've seen in a WHILE!