Unfortunately you are going to have an uphill battle to continue on to commissioning out of ROTC; however, there is still hope to be able to serve as a JAG in the future if that's truly what they want to do, which I will explain in a bit.
Humira is no small matter and isn't necessarily a first line medication for most conditions due to its significant potential risk; however, is an amazing medication when it is needed. That tells me that there is likely some underlying chronic condition that has previously been attempted to treat with another medication (now I could be way off here b/c the actual condition is not mentioned in this case.). Despite your son's stellar athletic performance that has about zero impact on what they will be doing in the future and the "issues" that are caused by an active duty member needing to take a medication such as Humira on a regular basis, or having whatever condition needs that medicine. If your son has a condition that has progressed to needing Humira I don't see an easy route to commissioning through his current program. It sounds harsh, but it is likely. To give some insight, when I was a flight surgeon I would have probably declined any person coming to the squadron who had a sea duty screening annotating the need for Humira (or any biologic for that matter).
Others have mentioned getting a second opinion, and potentially from a military physician. Certainly a reasonable consideration, I don't think it necessarily needs to be a military physician and definitely doesn't have to be someone with "operational experience." It just needs to be a competent physician who can either confirm or refute the diagnosis. It will then be up to the waiver authorities. If your son remains on the medication then the case will very certainly be sent to the active duty doc who is a specialist in the appropriate area who will make the determination. They will be well versed in the impact that a particular diagnosis or need for medication will have. (I get these on an occasional basis for eye issues). They don't necessarily need to have additional information from one of the other military docs. If it's easy enough to get into Walter Reed or Ft. Belvoir seeing they are in the DC area then go for it, but my guess is navigating into the Military Treatment Facility system is going to be extremely difficult, so I would consider heading for Georgetown or George Washington for a second opinion.
Okay, so that was the doom, and here comes the potential upside. As noted above JAG is usually not possible direct out of ROTC. If law school is truly what your son wants then I would take this as a sign to depart the Navy pattern for a bit, go to law school, and then apply as a direct commission JAG. The likelihood of getting a waiver for Humira as a JAG is higher than for unrestricted line. If he doesn't, well he's still got the Law degree, and if they do, well then he gets what he wanted in the first place! I would certainly not take this potential hiccup as an end-all, but rather maybe a sign to take a different path to the end goal.