Our dog has never had diarrhea but she has thrown up yelllow bile before. She too made the sound like you describe, the same noise cats make when getting up a furball. After asking our vet he has said it usually means she has gone too long without food. It always happened in the morning.

We now give her a Bonio before bed and it has 100% solved the problem. She has never been a big eater so it seems she is a little-and-often kind of gal.