My son developed hives after a course of antibiotics. I've never really know whether it was definitely related or not. I believe he has high histamine levels, as he does also have an allergy to wasp stings. The immunologist gave him antihistamine (which worked) and told him to stay on them, and he'd probably grow out of it.
We ended up going alternative and did cure him, albeit a little radical (hyperbaric chamber for an hour plus homeopathics, with a Doctor well known to friends). His hives were fixed immediately but he still does have a tendancy towards allergies. I have since found a wealth of information on symptoms of high histamine levels in the blood; (more apparent in males); it appears that it's not something the allergy doctors think of testing for. His thyroid is fine (although, I do note that hypo certainly makes us more prone to common allergies).
I have Hashimoto's and I started breaking out in hives a few months ago. I break out about twice a month and my lymph nodes swell. It is possible that it is just due to my thyroid antibodies, but my doctors are investigating otherwise. I have gone to a reputable allergist, who I trust more than my other doctors, and he cleared me for any and all allergies including an in depth test for celiac (gluten allergy). It's definitely not allergies, so again most likely it's my thyroid antibodies. I am curious to read further answers here. The only testing that is left for me is another thyroid scan, lymph node (mammogram and FNA), and in depth Lyme tests. Other than that, I have been cleared for any other health problems.
Thyroid problems can develop at any age.
There are many causes of hives, so it's impossible to say if thyroid is involved or not. However, with your family history, thyroid testing would be an excellent idea if only to eliminate it as a possibility.
Unfortunately, that will involve a visit to the doctor and a blood draw. There's no other way to be sure. Be sure your doctor tests FREE T3 and FREE T4, not just TSH.
Does your son have any other thyroid symptoms? Fatigue and/or drowsiness or insomnia? Weight gain/loss? Diarrhea or constipation? Brain fog? Elevated or lowered BP and/or HR? You can google symptoms to see a more complete list.