Can a 10 mth. old baby have a virus w/ just diarrhea & being fussy?

My 10 mth. old daughter is never upset. She was very fussy all day yesterday and around 6:00pm she has a very runny diaper. I didn't think anything of it but an hour later she had another and it was worse. She wasn't screaming or anything she just didn't seem happy at all. Well it seemed about every hour she had a dirty diaper until about 1:30am. But 2 days before she was sick I notice a rash on her bottom, which is bizarrd b/c she has never had diaper rash before. I'm just wondering if maybe that was related to it. She seems fine now but I'm a first time mom, so I don't know much about children sickness, help!