The severity of the vomiting, how you describe it, makes me think that possibly the chemo-receptor trigger zone is getting activated. A lot of people vomit when they work out, especially when they are new to exercise or have a particularly hard workout. That isn't abnormal. But the vomiting multiple times to the point of being hospitalized signals to me that something else is going on. If it continues, I would absolutely return to the doctor office and if they can't give you an answer, you may want to see a neuroligist or Gastro intestinal specialist. Also, certain medications can make you naseous and might make you more susceptible to vomiting on exertion, so if you are taking medication, this could be something to ask your doctor about (if they haven't already excluded that in the differential). If it gets worse, their are anti-emetic medications that prevent naseoa and vomiting. I don't know if that would be appropriate or not but again, your doctor may be able to help you with it. I would suggest going slow, staying hydrated and increase your distance/length of your run gradually. There is a possibility that you are getting motion sickness. Do you get motion sickness with any other type of activity? Again, their is medication that helps with this too. However, the whole point of exercise and running is to be healthy, so you don't particularly want to have to look to a drug related cure for the problem. I hope you start to feel better as you run and I hope you figure out the cause of the vomiting!