I don't know if this is timely enough to help, or even correct advise. When dogs or cats have a reaction to SQ vaccines, the recommended therapy is very warm moist packs, along with massage several times a day. We just had training at work last week on this very thing, and that's what the vet said to do. Like I said, this advise was for dogs & cats, so I can't be sure but would assume it would be the same for horses.
I wonder could it be that it didn't actually go under the skin, and perhaps went into the skin? This can often cause a reaction. Same protocol, though.