I wondered if, in this year when I might catch coronavirus, I should take my antihistamine for hayfever, or whether this would be a bad idea. Based on the Chief Medical Officer's public testimony, coronavirus causes a fever, five days of relatively normal immune response, then in about half of patients an extreme inflammation reaction which causes the most severe symptoms, and that by that time the virus is generally gone so that antiviral medication isn't effective.
In short, it appears that the answer is yes, an antihistamine would help. I can't be sure without official advice of course, but I'm sure enough that I will take my normal antihistamines this summer. I looked further.
I spent a few short hours reading up on inflammatory responses in lung viral infections[1], and it appears that lung damage in severe flu and other diseases is often caused by an overreaction by mast cells, a type of white blood cell. It appears that many fevers that cause problems due to inflammation seem to be caused (or at least correlated) in some way with an overreaction by mast cells. I was intrigued by the Dengue Fever description here: https://www.frontiersin.org/articles/10.3389/fimmu.2015.00238/full; that mast cells were beneficial in the first stages of the disease, but harmful in the later stages due to this inflammation response. Importantly, an antihistamine called ketotifen limits the action of mast cells in terms of inflammation, and in examples that I quickly found, seemed to almost always be beneficial.
Of course my scientific training boils down to one year of a 6-year degree course which only covered the basics of cellular biology, and my ideas are based on a few quick internet searches, but if I were a doctor today I'd try ketotifen as a coronavirus treatment during this later inflammation phase.