Good Morning, there is no need to be discouraged.
First, the HbA1c measure is of blood glucose over the past three months.
[edit: as Thud answered] Although it may show decreases sooner, the doctor should have waited three months to re-measure it. By its very design, a decrease would have been unlikely in only five weeks. And up or down a few points can be normal lab variations.
When do you "test everyday"? and 20 points over what? 100? To get good information about the foods you are eating, suggest doing pre and post-meal BG tests. You go through a lot of strips but they can be purchased cheaply on-line.
Find the previous two threads you started. This one and the one in Intro. https://forum.lowcarber.org/showthread.php?t=482459
I had many questions about the food you are eating...do you cook or do you eat in a central dining room? If so, you need to ask about the foods purchased and how prepared. If you have been eating scrambled eggs...are they made from processed dried eggs to which starch has been added as a thickener? you may find the hamburgers are low fat with additives, or sugar is added to cooked vegetables, any number of surprises with institutional food. Basically you need to see the labels on purchased foods, check recipes, and count the total carbs of foods you choose to eat. Call me suspicious, but your diabetes diagnosis a few years after moving to independent living may not be a coincidence.
There are a number of previous threads on Metformin in the diabetes sub-forum, and GI distress can be one side effect. If you are not on any medications at this point, I would suggest trying very low carb (20g total carbs) first and giving diet and lifestyle enough time to see if your BG can come down further. Example, check all your carbs for a few days to see what you are eating now, but there would be no rom for a "few hamburger buns"