There are at least two things you wrote which are generally medically incorrect.
Well, but then again you didn't fair much better...
First of all, having only a stomach ache after ingesting a drug is very unlikely to be an allergy. True (IgE/T-cell-mediated) allergies usually cause things like hives, throat/lip/face swelling, low blood pressure, and trouble breathing.
No. Not even remotely true. Most food allergies do not lead to such severe symptoms as you list. In fact, that list of symptoms are clear warning signs that an anaphylactic shock is imminent, and you should prepare yourself accordingly. Most gastro intestinal allergies are much milder in symptoms, and can actually be difficult to diagnose as a result. And furthermore, most people with food borne allergies do not have serious symptoms from the rest of the body, with their gastro intestinal tract feeling A-OK. It's the other way around (with the exception of skin involvement, that's usually a greatly delayed response though).
So no "tell tale symptoms" unless the allergy was severe. Most are not. Which is a good thing since about 5% of the adult population suffer from some form of food borne allergy.
True allergies are generally not heritable either, so the "my relative was allergic to X, so I can't take it" is nonsense.
Could be argued technically correct, but that's the worst kind of correct. In fact, the tendency towards allergy is strongly hereditary and the same major organs also tend to stay involved, i.e. a family with gastro intestinal issues tend to have that passed on, and a family with respiratory involvement tend to have that passed on. (This is a weaker tendency though, hayfewer in both parents could well lead to a food allergy in their offspring).
The exception to this is in people who have things like celiac disease who have a T-cell-mediated response to gluten in the medication which is an allergy
Nope. Celiac disease is not an allergy. Completely different part of the immune system is involved in that one. (Well, OK, not "completely", but different enough.) It's quite possible to be allergic to many of the wheat proteins without suffering from celiac diseas, and vice versa (though wheat protein allergy is uncommon, and an allergic reaction to gluten as such, without celiac disease si extremely uncommon.)
That said, you are correct that people reporting an adverse reaction to some immunisation (flu being typical) are mistaking the effects of adjuvant factors that are added to the vaccine to give it better punch. In fact, they're there to strengthen the immune response (which makes you feel sick). That's nott to say that you cannot be allergic to shots and what's in them. It's not for nothing that about 3/4 of all anaphylactic shocks happen at the doctor. They're the ones injecting stuff into you.
And also, due to the base-rate fallacy/class imbalance problem it is actually less likely that the grandparent is allergic to opioid than having any of the other well known reactions. Checking for that is as easy as getting a blood sample and check for antibodies (a test that has a fair, but not perfect record), so since knowing about an allergy of that nature could be very useful (lest one gets a shot of morphine during e.g. a car accident) getting that test done would probably be a good idea.