Rhianon, don't worry about the not eating. That's really common when they aren't well. Try giving him some extra bfs if you can. The bm is probably the best thing for him, and will definitely be the easiest thing tolerated by his tummy. Runny noses often cause upset tummies due to the mucous running into the tummy - adults can get this too.

The main thing to watch for is signs of an ear infection or throat infection. These can happen after a few days of a runny nose and do need to be treated. Other than that there's not a lot you can do. It sounds like you are doing a great job. I hope he's better soon.