Honestly I don’t think you have too much to worry about with corals specifically. While your medical history is unclear, here’s my two cents.
I would break medical concerns down into two categories. 1) sensitivity to things, and 2) immunosuppression. Generally, sensitivity arises from an over-reactive immune system. Asthma, having a lot of allergies, reactive skin, those kinds of things. If that’s what we’re talking about then you should wear a good pair of shoulder (or elbow, sounds like you have a small tank) length gloves regardless of corals. Skin can react to anything in the water including the saltwater itself. I’m not reactive at all, but I’m very conscious about putting my hand in the tank based upon the last time I put lotion on. So I think it’s not as hard to forget the gloves as you might think.
As others have stated “danger” from corals comes in two varieties- stinging cells, and toxins like zoanthids. Both concerns are very small generally, but if you’re hyper-reactive, it’s best to avoid contact with the marine environment. Zoa toxins for instance- unless you’re fragging (putting it under stress) and/or have open wounds, the chance of getting sick from just having your hand in a tank with a zoa is pretty much zero. Not enough toxin in the water, or absorption in the body.
However your post to me suggests number 2; immunosuppression. Immunosuppression by itself doesn’t increase the danger from either stings or toxins. In fact with some toxin exposure such as in anaphylaxis, the immune system isn’t the solution, it’s the entire cause of the problem. Having a poor immune system has zero to do with dealing with mild stings or toxins. In fact it’s category 1 that has to worry about reacting to mild stings. If very immunosuppressed what you should be concerned about isn’t the corals...it’s the Petri dish of bacteria living in your tank! And only then for the most part, if you have any open wounds. Corals don’t kill immunocompromised people; bacteria and viruses do.
Even if you fall into category 1, IMO the danger from most corals is minimal. Maybe don’t get a super aggressive anenome and handle it with your bare hands, but the chances of having a severe allergic reaction from casually brushing by a soft coral the one time you didn’t wear gloves is extremely unlikely. Enjoy the hobby, try not fear it!