My daughter vomited with no signs of sickness which had a destinctive odor unlike bile or normal vomitus. she also has painfully bowel movements. help?

Many reasons: She may have eaten something that didn't agree with her. This might be the first sign of a virus. Pain with bm might be as simple as not enough water or fiber. I can't give a more specific answer based on just the info you provided, but i can recommend that if this continues or worsens you should have her evaluated by her pediatrician.