Baby having multiple diarrhea diapers in a day!

For the past few days my baby has been having multiple diarrhea diapers and he has a bad diaper rash because of it. I've been frequently changing diapers, lathering his butt up with diaper rash cream, trying to let him be naked as much as possible, and letting him soak in warm baths but his rash hasn't gone away because he keeps having blow outs. I'm not sure what is causing this...his diet hasn't changed and he doesn't appear to be sick otherwise. What do I do?