Could my back pain be caused by my ms?

Rarely, but yes.: Depending on your extent of disease and location of neuronal damage, group of muscles affected, it is very possible.

Doubtful: Back pain can be caused by multiple events, but MS does not usually cause back pain as a symptom, and certainly does not present this way. If you have recently started the MS drug Gilenya, (fingolimod) back pain could be a transient adverse event. Otherwise search for a pain generator, and get this managed.