Yes. You should not be throwing up regardless of what you may have. If you have had diabetes for a long time (especially if uncontrolled), you may be having "gastroparesis", a condition in which there is delay in food emptying from your stomache. If you have type I diabetes, you have a 5-10% of having gluten allergy (celiac disease) and simple test can rule it out. Talk with your endocrinologist.
Yes. If you are getting dehydrated or feeling weak go to ER.