It is possible...
I have allergies to grasses and milk products but gunpowder residue does not bother me.
However, as a precaution I always wash my hands immediately after a range session before I even leave the range. Then, I go straight home and take a shower and put on a fresh set of clothes. If the allergies manifest with sinus reactions, or lung reactions, I recommend using a respirator while shooting; especially in confined indoor ranges.
These precautions should help minimize any effects of allergies to gunpowder residue.
Clinging to my God
and my guns!
Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.