Too many shots too close together in too young of patient. One shot today are actually several in one. It's not just in kids but animals where issues show up. I have a Toy Rat Terrier. I took her to the Vet for her annual shots. A week after the shots she broke out in welts so severe it took a benadryl shot to stop it by another Vet because it happened on a weekend. I contacted my Vet about it and he said likely just happenstance or a reaction to an outside plant, weed, etc. The next year I delayed her shots by a month and same reaction same shots. Again he danced all around putting any blame on the shots. Now I have him give her a Benadryl shot before any vaccines and I give her at least 2 doses or oral Benadryl daily for a week afterward. Even with that she shows some reaction signs.
Vaccines effect the autoimmune system of course reactions are possible and severity may be unpredictable. I've taken allergen shots for about 12 years now. Each time I must sit in the lobby at the doctors office at least 20 minutes in case of adverse reaction.