In the early days of Copaxone, and Betaseron I had this low level humm of nausea. not bad, not wretching, just this humm that followed me through my day. it was upsetting. it took about six months, but it did go away.

many things can cause nausea, from meds, to stress, to exposure to chemicals. If your nausea is severe, meaning it is interferring with the ability to live your day to day life, you need intervention. If its just this low level hum, give it a bit and see if it backs off.