It sounds scary, Stephy, but it doesn't sound like diabetes, because your blood sugar would be consistently higher. I did some reading on Vasovagal syncope, and that does fit your symptoms. Check out these links:
http://www.mayoclinic.com/health/vasovagal-syncope/AN00103
http://heartdisease.about.com/cs/arrhythmias/a/Syncope3_2.htm
Take this information to your doctor and ask about treatments, and perhaps you should look into a specialist. It sounds like a very frustrating problem, but hang in there and seek treatment. If you remained concerned about hypoglycemia, seek out an endocrinologist, who can run the appropriate tests.
Good luck.
You probably should be tested for hypoglycemia just to find out if this is part of the problem. If the problem is indeed vasovagal syncope, then the treatment for that condition won't touch any additional problems with hypoglycemia. So hypoglycemia probably should be ruled out so it does not complicate the issue.
If hypoglycemia is suspected, then you should try to keep some sort of juice handy and drink a small quantity if you start to feel "off" at all just so as to make sure that this is not the cause. I happen to be a tightly-controlled diabetic who occasionally does find myself hypo and I have learned to really listen to what my body is telling me. MY symptoms are NEVER wrong, even if when I test my glucose levels, they come back normal. I can feel the symptoms when a glucose drop is in progress, before the glucose levels actually become low. So I have learned to treat the symptoms when I feel them in order to prevent severe lows from happening.
In your case, you may want to ask your doctor to check you very thoroughly to see if hypoglcyemia is indeed a big part of the problem (heart rate can speed up during a hypoglycemic episode, by the way). If not, then you may want to see a specialist to see if you can be treated for the vasovagal syncope problem.