Is my baby sick? :-S?

I think you should make an appointment sooner..just in case. That kind of poop doesn't sound quite right to me. Black in the baby's poop is sometimes not a good thing..could be signs of internal bleeding. I would definitely make an appointment sooner to rule anything out that could get worse. The vomiting is very concerning as well. Something's not right. Follow your mommy instinct...get help for her....