It does sound like an allergic reaction and the vet was right about the edema it will go to the lowest portion of the body on geldings/stallions that is the sheath/shaft. If the shaft is swollen also and he cannot retract it my vet told me to make a sling( jock strap) I used an old bath towel and some old reins. I cut 2 holes in both long ends of the towel ran the reins through the holes in a loop on the first side the towel went underneath our horse while the reins went across his back/hips I then ran the loose end of the reins through the 2nd holes and tightened them up enough to support him without restricting his ability to urinate and tied them off. The idea is to elevate it to reduce the amount of edema so it doesn't cause more damage as the skin is very sensitive and soft there and it can swell so much that it begins to split which can cause infection etc. We did this after the vet had worked with him for over an hour massaging( yes that's what he done lol) the sheath/shaft to try to relieve the edema that did work some but we still needed to get it elevated to keep it from doing it all over again.. I unfortunately wasn't dealing with an allergic reaction my old man had cancer. A tumor was pressing on a nerve blocking his ability to retract his shaft, he could urinate but had no control over it other wise sadly 2 days I opted to have him put down. He was 24 and had lived a wonderful life I did not want him to suffer and treatment at his age with no guarantees of a cure did not seem feasible.
Courage is being scared to death but saddling up anyway~~John Wayne