Below 100 is normal. So, only the one reading you stated that was at 100 (the minimum to be considered a prediabetic number) has happened. I would try to relax. Your A1c was also normal. Type 2 diabetes can be prevented in most people. You sound a healthy weight. Do you exercise as well? And then as your doctor suggested, a diet with less sugar would be wise. There are easy things to cut out like soda, processed foods, etc. Low fat protein, vegetables and whole grains are healthy choices. While I guess your concern is your numbers are inching up, they are not any super red flags here that you will definitely develop type 2 diabetes so just be aware to lead a healthy lifestyle. good luck
A1c of 5.6 is an average blood sugar of about 120. It is strange that your meter is only reading in the 70s and 90s.... could be that your meter is reading low.
A1c of 5.7 corresponds to pre-diabetes. This means you are pretty close.
Best approach would be to keep monitoring (a1c every 6 months), and occasional checks after eating (try testing at 1 hour and 1.5 hour to catch when you go highest) and fasting.
Please focus on eating lower carb foods, which should also help in prevention. The popular paleo and keto diets can be useful in this regards, though I don't recommend you go overboard with fats as some do with keto... continue with exercise.