Is my newborn sick?

Ariel

He's 5 weeks old and was born prematurely at 35 weeks. He's been throwing up and having diarrhea for almost a week. He's formula fed and his temp is 99.1 and I know that's possibly not a fever for a newborn. But I'm concerned with his spitting up. I was in the hospital for a week and my family was giving him rice cereal and gas drops. I told them not to and stopped it immediately. I've been home for two days and he still has diarrhea. He's very fussy and cranky. Should I take him to the ER? I know he can get dehydrated really quickly.