Under 90 is normal so you are high. What "diet" did he say to use, probably low fat. Unfortunately its not fat that raises BG but carbohydrates that raise BG (blood sugar). All carbs raise BG, reduce carbs have lower BG.
fasting blood sugar in the range of 120 - 130 puts you firmly in diabetic territory, as does your hba1c of 7.4 which corresponds to an average blood sugar level of about 180. These levels would already require medications.
Consider that normal fasting should be below 90 and normal hba1c is < 5.0.
Given your height and weight, you are not overweight. Further you have no family history of diabetes. Therefore, I believe you should be evaluated for adult onset type 1 diabetes. This would involve evaluation of c-peptide, antibodies, and insulin levels correlated with blood sugar levels. Type 1 is lack of insulin (and needs injected insulin), Type 2 is plenty of insulin, but there is insulin resistance and the insulin is not effective. For Type 2, oral meds may be appropriate.
If it is adult onset type 1, it may develop quickly. Therefore, I suggest your read up on syptoms of both type 1 and type 2 and if you develop symptoms then you must go to your Dr. or even the hospital.
Do you have a home meter? You should test fasting and then 2 hours after starting to eat. You can try modifying your diet. The optimal approach is very low carb, moderate protein, and enough healthy (nonprocessed fats) that you are satisfied and maintaining your weight. By testing after you eat you will be able to see which foods send your sugars high, and which don't and modify your diet accordingly.
I will recommend this site: Bernstein Diabetes University (on U-tube). He also has a book called Diabetes Solution. Bernstein is the father of modern diabetes management and a very strong proponent of low carb to manage diabetes.