I am not the right sort of doctor, and you
should ask a medical professional. My knowledge comes from
very out-of-date experience working in a computational drug discovery lab, which gives one a very narrow view of a very small number of things.
Seriously, ask a doctor, but these might give you starting points for the discussion:
This is a very high-value part of pharma research, because inflammation is at the root of a lot of lifelong chronic disease and is basically only manageable rather than curable. But because inflammation is a systemic response, all drugs which modulate the immune system are serious business.
For short-term use: corticosteroids (eg prednisone), and I think best-current acute Covid pneumonia protocols involve quite a lot of these, particularly dexamethasone (https://www.covid19treatmentguidelines.nih.gov/immune-based-...). Corticosteroids are extremely powerful drugs. Some of them are used topically for acute local inflammation (hydrocortisone is the best known of those and is available OTC from pharmacists for rashes), but that's basically the only context you're likely to encounter them taken as lightly as, eg, aspirin or acetaminophen.
Long-term use; there are some small molecules, eg methotrexate, which modulate the immune system – hydroxychloroquine is one of these used in lupus treatment, but there is plenty of evidence that it harms rather than helps in the Covid case.
That leaves you some of the second-line treatments used for chronic immune system diseases like rheumatoid arthritis, Crohn's disease, and ulcerative colitis, and there the Lancet paper I linked up-thread suggests these may have some utility/protective value against Covid, found by studying correlations in patients undergoing these therapies for pre-existing conditions.
But: these are not easy options. They're "biologics" (big proteins). You've had or know people who've had some of these. The ones you've probably encountered are vaccines and insulin, but the big growth area has been monoclonal antibodies. Some of these can directly modulate specific signalling pathways, particularly inflammation pathways, which is why they are effective against the diseases of systemic inflammation above. But: these drugs are extremely expensive to develop (so the US prices are ungodly high), difficult to transport, store and deliver - often requiring IV infusion (I think Humira has a self-injectable formulation, but none of them are oral medications) - and have systemic side effects basically by design.
Two new monoclonal antibody therapies of this class have US EUAs (emergency use authorizations) for Covid; https://www.fiercepharma.com/pharma/regeneron-following-lill.... One of them (the Regeneron one) is the one Donald Trump had.