A dog can have diarrhea and vomiting at any time. It is never normal and you should defiantly keep an eye on your pup to watch for changing or different symptoms, you need to be especially aware of dehydration with can be caused by these two things. I would highly recommend having your dog spade.
You should see your vet ASAP. Neither of those is associated with heat. Aside from many other issue's it can be, many people can mistake the sign's of open cervix pyometra (deadly uterine infection) for heat and/or pregnancy. It may also be some other serious problem which happened to occur during her heat. Hope your pup is okay.