Have you been following any of the science over the past 15 years on epigenetics? Originally rejected by the establishment medical community, it's now been heavily embraced by most and has been featured in news magazines and medical TV shows, plus medical journals. The reason I bring it up is the family history of allergies. Epigenetics has shown that there is not a pure genetic basis for the vast majority of medical issues and allergies (meaning the DNA) but rather there effects on the epigenome (the part "above the genome" where gene switching occurs, turning on bad genes and turning off good ones). The most recent science is showing that these epigenetic changes can be passed on to the next generation - which is the family history part. This is good news, because it means that our genetic expression can be affected and reversed.
So while I would look at the oatmeal with cinnamon & apples (perhaps a premixed product?) and consider using whole foods that you mix yourself, we are also faced with contaminants, GMO foods (controversial), and other environmental factors. There are higher standards in the infant food industry (particularly with formula but often with other products), which may explain why the infant oatmeal was okay and this new oatmeal is not. Another factor is additives. The facts are that he has some food issues, some breathing issues, and there is eczema in his sister are all indicators to me that this is highly reversible. I work with people all the time with these issues - breathing treatments, nebulizers, eczema/rash issues, and food sensitivities. Most can be reversed. Anaphylactic reactions are, of course, extremely serious, and while it may be that those kids (and adults) can never eat the trigger food(s), in most cases they can be brought to the point where accidental exposure or cross contamination does not cause a life-threatening reaction.
So you could certainly pursue another route, since the medical route (with medication) has not done anything much for him. (It usually doesn't because it's only treating the symptom and not getting to the epigenetic source of the problem). This is much easier, more reliable, and far less stressful than extensive testing and elimination diets. It's a viable option. It also improves immunity and does so much for prevention of multiple issues, including inflammation. Inflammation is at the root of most conditions, and especially those that you have indicated (asthmatic type responses, intestinal issues related to food reactions, and skin rashes). These autoimmune responses are all going to respond to simple additions of epigenetic agents to reverse the reaction. It's a non medical approach that does not interfere with any medications that may be prescribed, now or in the future, and with zero side effects.