D.B.
Yes, I would supplement to boost the immune system and reduce any inflammation that may be contributing. There are phenomenal research results with lunasin (see lunasin.com) which is a naturally occurring soy peptide with phenomenal results in many areas, including cell repair and prevention. There is only one company authorized to work with the lead researcher and discoverer of lunasin (in the 1990s) and in collaboration with the growers and the team doing the extraction of the lunasin from the soybean and concentrating it. There are a couple of ways to get this premier lunasin, either through a comprehensive supplement (patented which means safe, effective and unique) for kids (he's still in the kid phase but he can transition in a couple of years to the adult formula), or through a capsule, or both. The capsule just has the lunasin, the other has lunasin added to vitamins, minerals, etc. and would replace any vitamins he's taking.
I do not advise going into a supplement pill and particularly not a gummie - not absorbed more than 15-30%, can cause stomach irritation. You don't want any more irritation in this child (not that you want it in anyone). Premixed liquids don't usually hold up - short shelf life - with a few exceptions.
You can buy cheap lunasin anywhere but I don't recommend it - everyone's jumping on the bandwagon but the processing can weaken it or include stuff that's not so safe, and a lot of it is from genetically-modified soy. Still, I get it for $22 for 30 capsules - made in the US and in conjunction with the key scientists working on this. I can't say enough about it. Happy to give you more data if you like.