My dad was allergic to codeine, so I'm guessing he would have been allergic to morphine too, since they're both opium drugs. He had a bad cough and the doctor gave him codeine cough syrup for it. Made him sick as a dog. He was throwing up for a couple of hours -- until it all got out of his system, I guess.
Morphine makes me nauseated, but I don't know if that's just a side effect for me. They gave it to me after I had surgery and it made me sick. That was especially fun after throat surgery. Blechh.