Hi, So I Have A UTI And I Was Prescribed

Hi, so I have a UTI and I was prescribed a penicillin based medicine yesterday, which caused me to puke and have diarrhea. I was having diarrhea all night and called my doctor to get a new prescription. The new prescription is Cephalexin. I understand that vomiting can come as a side effect of this, and I have not eaten much today since my stomach is still feeling a bit questionable. I am extremely scared to take it for the fear of vomiting. Is it safe to take under my conditions?