Byeta is a class of drugs called insulin mimetics. This includes Byeta/ Bydureon, Victoza,
Januvia, among others. Maybe your Dr can check if any of the others are covered and may be of help for you.
If you cannot get these drugs, you may want to try a low carb diet (low carb, moderate protein, and fat for balance of energy). Some people find this way of eating helps both blood sugar control and weight management.