I've had this problem from time to time, and I know from other posts I've read that other 3 under shooters do to, to a greater degree than split finger shooters, at least from the number of posts I've noticed.
Once you start bleeding, any little touch will start the bleeding again, so it might make you think you have a worse problem than you really do, and might also make you start lifting up your head when you shoot as an involuntary response, which is a bad habit to get into. So do whatever you need to do to avoid hitting your nose until it heals, including really exaggerating the rotation of your head if you need to.
Switching from a tab to a lightweight glove helps some 3 under shooters to avoid hitting their noses.
If you're not getting your elbow all the way around behind the arrow at full draw, the outward angle of your forearm can cause some sideways forces that can result in the string hitting your nose on release.
Fortunately, rotating your head and getting your elbow behind the arrow are good form, so as you're solving your nose problem, you may also improve your shooting in general.