HbA1c is glycated haemoglobin which is testing how much glucose has stuck to the red blood cells, and it’s sort of an average of the last 3 months, because that’s how long red blood cells live. The higher your blood sugars have been, more will have stuck to the red blood cells. The finger prick test is measuring how much glucose is floating around in your blood at this moment. Try not to compare them as they are testing different things, although the higher your finger prick tests are normally the higher the HbA1c will be.
Why were you told not to test at home? The usual reason given is that people can become stressed out by the numbers, which may be true in some cases but not all, and to be honest it’s more likely a cost saving exercise because the strips are expensive. If you’re curious though and want to help yourself, the most useful way to test is immediately before you eat and then 2 hours afterwards, and if you’ve gone up by more than 3 there is too much carbohydrate in that meal for your body to cope with. Then you can start to look at swapping potatoes and rice for more green veg, or reducing portion sizes, and so on.
if you can be fairly strict with your diet your HbA1c should start dropping fairly quickly. I think there is some suggestion that you shouldn’t try to drop it down too quickly as that can cause other problems, I’m less familiar with that though, I just know that your body needs time to adjust to the new levels and you can feel pretty awful if your sugars are much lower than they have been for a while, even if they aren’t technically too low. I’m more familiar with it from a type 1 point of view though, hopefully some type 2s will be along in a while!