It's not just 'sugars' you need to avoid, diabetes is an inability to process glucose properly. Carbohydrate converts, in the body, to glucose. So it makes sense to reduce the amount of carbohydrate that you eat which includes sugars.
The main carbs to avoid or reduce are the complex or starchy carbohydrates such a bread, potatoes, pasta and rice also any flour based products. The starchy carbs all convert 100% to glucose in the body and raise the blood sugar levels significantly.
The way to find out how different foods affect you is to do regular daily testing and keep a food diary for a couple of weeks. If you test just before eating then two hours after eating you will see the effect of certain foods on your blood glucose levels.
Buy yourself a carb counter book (you can get these on-line) and you will be able to work out how much carbs you are eating, when you test, the reading two hours after should be roughly the same as the before eating reading, if it is then that meal was fine, if it isn’t then you need to check what you have eaten and think about reducing the portion size of carbs.
When you are buying products check the total carbohydrate content, this includes the sugar content. Do not just go by the amount of sugar on the packaging as this is misleading to a diabetic.
As for a tester, try asking the nurse/doctor and explain that you want to be proactive in managing your own diabetes and therefore need to test so that you can see just how foods affect your blood sugar levels. Hopefully this will work ! Sometimes they are not keen to give Type 2’s the strips on prescription, (in the UK) but you can but try !!