Most of the sea-sickness medicines are available over the counter. One that is popular is Antivert (meclizine), and it works pretty well, but the main side effect is drowsiness. A few years ago (pre-MS), I had a bout of vertigo for a few days. It was the weirdest thing, and the docs suggested it was benign positional vertigo, maybe brought on by a virus. (Of course, looking back, this may have been a first sign of MS). Anyway, they prescribed Antivert, and it worked pretty well. There's another over-the-counter med called Bonnie, that I think doesn't cause drowsiness. I'd check with your doc on any possible interactions with the Avonex.
Another (natural) remedy that I've read about is ginger. You can buy the root at some grocery stores, and suck on a piece, or make tea out of it. I think ginger pills are also available. Don't know how well the ginger works, though.