Norovirus is awful so I hope you're starting to feel better. I didn't have that virus but I did have a 'flow through' situation going on after I had some surgery recently. I cut my metformin off on the days I didn't eat anything then went back to just two a day as I started to recover (from 4 but my bloods are so improved of late the docs said fine to cut to two).
Have you been testing to see what your levels are at? Sorry don't want to assume you have a meter or are regularly testing. Illness can send your levels sky high even if you're not eating so it's worth being aware of the fact. Metformin is one of the drugs that should be ok even if you don't have food in your system (there are other diabetes types that aren't so good if you're being sick or haven't taken food), though it causes me stomach upset if I eat them on an empty stomach. And of course if you're still in the full flush of the virus you won't really be keeping anything down!
Once the virus clears you need to leave two days before interacting with others too so you don't infect them. I hope it does clear soon. When you can start eating simple foods (scrambled eggs is always a nice one) and maybe ramp up your metformin again slowly to give your system a chance to recover. I hope you're feeling much better really soon!