Without meaning to pick on the OP (but wishing him a speedy recovery), I think this might have been different if he had been stung while at the firing line. Most of us drill into our heads that whether it's a stoppage or hot brass down our shirt, the muzzle stays downrange, and if necessary we will shelve or holster the weapon.
Similarly, friends and I have had bees go inside our shirts, vests, or jackets while riding motorcycles. In all those cases, we pulled over first, then dealt with stinging critters.
I think people need to gear their minds, ahead of time, that a fall from a tree stand will be worse than even multiple stings (with the rare exception of those allergic types who are likely to go into anaphylactic shock), and the first reaction to any problem has to be "do not fall".