I would strongly be suspecting that your family has an allergy to either horses or eggs.
Most vaxs have either eggs or gelatin in them...so people with mild to severe allergies tend to react badly to them (rashes, long fevers, all the way to seizures and anaphylaxis)
Go to an allergist and get tested. It could be that the allergy is mild enough not to impact your eating habits because ingested the effect is pretty mild, but shot directly into muscle, fat, or veins your histamine response goes through the roof.
It's not uncommon (the paperwork you sign asks specifically about those allergies), and there ARE alternate vaxes without them, but the have to be special ordered and are more expensive. Insurance won't pay for them unless there is a stated or documented allergy.