Ours is just over 2. We had similar issues when he was little. Also ending up in hospital once.
You said he didn't test positive for alergies, but diet seems to have helped us this year with no new huge issues.
We cut him back to just basic food. Meat and veggies (as much variety as possible) and then added things back slowly.
Based on when he started getting sniffles, we now limit his gluten and dairy to occasional treats. And it seem's to be working so far.
Maybe he didn't eat the offending in the uk.
Maybe youve already tried this. Or This might not be your issue, but it's not hard to try, and won't cost anything except maybe a bit of time to prep non-cereal breakfasts. (Depending on your current habits)
Just offering our personal experience.
Eg When he had a bout of cake and biscuits at school over the clurse of a week, he had sniffles again. Cutting out his 'treat' for a few days and he cleared up pretty quick.