My first response is NO - this is not normal. Pain is typically a signal from your body that something is not right.
However, when we're talking about living with MS, pain is too often part of the package. There is something called the "ms hug" which has been described as extremely painful. But I've never heard somebody describe it as feeling like a tightening pain UNDER the rib cage, only over the rib cage.
I think that you should definitely contact your doctor to be evaluated. If something else is going on, then you shouldn't delay.
could be numerous things..see a doctor soon