My motto is test Test TEST.
Start by testing before meals and at least once after meals, it is recommended that we test 2 hours after taking the first bite -- not 2 hours after finishing the meal..... Someting I tried was to test at hourly intervals such as 1 hour 2 hour 3 hour and 4 hours after my meal to track the rise of my sugars and when they start to return to normal..... It was a healthy tool because I found that my high is not at 2 hours like most people, it was more like between 3 and 4 hours....
Try to never let your sugars drop too much. 39 is was too low. When you go that low, you are risking going into a diabetes coma and unless you are coherant and can get some glucose into you, it can lead to *___* Going too high will not kill you right away, but you are doing damage to all of your organs and that can come back to bite you in the long run.
The only way to avoid either pitfal is to spend time to plan your meals, set up regular eating times and stick to it. As the Lady Mary says, drink lots of water as this will help the body flush those excess sugars (and salts) out of your system. If you work outside the home, become friends with your pressure cooker and crock pot so you can eat shortly after getting home.
You asked if it is better to go wheat free or use the diabetic diet. I do not see a need to go wheat free unless you are celiac and cannot have gluten. On the other hand, use moderation and portion control..... Personally, I find that the diabetic diet as recommended by most nutritionists, has way too much carb for the average diabetic but the only way to know for sure is to test, Test TEST..... Also make sure you spread the carbs throughout the day, not have them all in just 1 or 2 meals......