Should I be worried about my great dane puppy's diarrhea?

My 12 week old great dane puppy has been having soft stools on and off this week. Today I switched him off of his puppy food to rice, and he has been drinking just fine with no vomiting. He seems to be acting like himself, but the frequent diarrhea today is worrying me. The vet said to try three days of chicken and rice and call if he vomits or gets lethargic. Out of curiosity I checked his heart rate, and it was at 160 at rest. i don't know whether I am being a paranoid puppy parent (I am the worrier of our family), but I am wondering if he should go into the vet.