When you say that the pain shifts, this leads me to think its your nerves. If pain persisted in your lower abdomen while the pain in your armpit comes and goes, then that would be a different story. Now there isn't a major nerve going from your abdomen to your armpit. So the problem probably isn't a pinched nerve. Instead, the nerves extend from the spine like ladder rungs. So I'd have to guess it might be a more general inflammation, either along the spine or along the left side of your body. As you move, breathe, digest food, etc., pressure can be relieved in one location and subsequently added in another location.
As for the cause of the inflammation, it's hard to speculate. Some possibilities are wearing a heavy backpack only on one side, performing a repetitive activity such as shoveling, or even stress induced muscle tension. When these muscles become inflamed, they squeeze on the nerves causing pain in whatever area the nerve services. If this sounds probable, then potential solutions could be some gentle stretches to relieve some of the pressure on the nerves, taking over-the-counter anti-inflammatory medicine, and refraining from the offending activity. As with any diagnosis you seek here, you should ultimately speak with your doctor for a more conclusive answer.