Reading John Williams Augustus at the moment, there is a heavy focus on a illness in 23BC.
"All his life he experienced at certain times dangerous fits of sickness, especially after the conquest of Cantabria; when, his liver being injured by a defluxion upon it, he was thrown into such great discomfort that he was obliged to undergo a desperate and doubtful methos of cure: for warm applications having no effect, his physician Antonius Musa, recommended the use of cold." - Suetonius
Are we sure it was his liver? He was sick many times, so perhaps influenza. Did Musa's cold bath treatment honestly work, i understand little about cold shock treatment and I'm not sure if it helps with the flu or liver problems? Thank you
I wonder if this might be better asked on /r/historyofmedicine? It might at least be worth a crosspost.
As a doctor when I hear "repeated episodes of pain around the liver" my first thought would be biliary colic (attacks of pain caused by gallstones obstructing the release of bile). They wouldn't be likely to afflict him "all his life" though. It tends to occur in middle age. But it's possible they meant "all his life as ruler." And it's a very common condition so relatively likely. Inflammatory bowel disease such as Crohn's disease or ulcerative colitis would be a possible diagnosis that could start much earlier.
There's really not much to go on from the passage you cited though. Are any other symptoms ever mentioned?
As for application of cold (and heat as was mentioned to have been tried first), you might get some analgesic effect. But that's really about it.
Edit: apparently the illness which affected him in 23 BC was also afflicting others, so am infectious disease would be the obvious concern. I'd wonder about either malaria or possibly typhoid fever. Not sure if this Romans of that time recognized these particular illnesses or a have just called them fevers.