I'd heard of something like this for fevers, but not for vomiting. Very interesting! Have you read this?
cyclic vomiting syndrome - Bing Health
Be prepared for your doctor, (and 17 more after that!), to tell you you're crazy. BTDT!! Stick to your story, though. Keep a very detailed journal. Write down anything and everything that happened the day before (foods, drinks, activities, stressors, seasonal allergies, etc.), even if you think it's not important. Try to see either a gastrointerologist or an infectious disease doctor. You may even want to see neurology and/or endocrinology in case these episodes are being triggered by migraines or seizures.
I hope you get an answer and that it goes away sooner rather than later.