Well, you definitely should CHANGE doctors to one that looks after your health. A doctor who refuses a patients test request, especially one who thinks your weight does not apply to diabetes, is not one that is looking out for the best interest of the patient.
Try to get a referral to an Endocrinologist, a diabetes specialist, as most primary doctors are not well versed in diabetes prevention nor care. Your current doctor is a good example. Also, get glucose tablets. Take one when feeling dizzy/faint or lightheaded. This will raise your glucose levels. Do not over due it as they are for emergency use only.
These are the tests you should request from your new doctor. Be sure to get a copy of the lab results for your own records. Lab result sheets are marked with low and high ranges, or < [less than] indicator for each test. You want to fall between those numbers or be below the number.
1. A1c - Measures your glucose levels over the past 3 months. The test result is presented in % [percentage]. Normally used to test for Hyperglycemia.
2. Thyroid TSH test - An abnormal thyroid will disrupt your glucose levels.
3. Since you show symptoms of acute Hypoglycemia, the C-Peptide test is recommended. It is used to monitor insulin production and determine the cause of hypoglycemia.
4. GAD antibody test [not to be confused with GAD test for anxiety]. Autoantibodies and GAD is found in Type1 Diabetics prior to disease onset.
Take the time to Google and learn about Hypoglycemia and also LADA [Latent Autoimmune Disease in Adults] which is a type of Hypoglycemia and often misdiagnosed as Hyperglycemia.
Good luck.
Weight has nothing to do with, if your diabetic or not. As for you Hgb(iron count), 20 is way too high. Normal range of Hgb for women: 13-16mg/dl. I don´t know what type of physician your seeing, but you do have some diabetic symptoms and this "physician" is not capable of observing symptoms nor does he have medical criteria.
Recomendation: Buy a personal blood glucose unit and monitor your results. Get in contact with a new physician and report your old physician to your local Medical Board!