Hi! I'm not a medical professional, just the parent of a kid with diabetes. Even health kids and adults get temporary spikes in blood sugars, so 165 is very likely a normal number, particularly with the number of carbohydrates in the meal he ate. I think he's fine, I wouldn't be concerned, but it's always prudent to check blood sugars if you have concerns.
The 165 post-meal suggests that he has insulin and it's working. I would follow the Doctor's advice and test periodically, but I wouldn't worry about that number at this time. A blood sugar (BG) of 165 fasting would concern me but not 2.5 hours post a high-carb meal.
The bedwetting is a different story. Did you test his BG after those incidents? I took my then 6 year old in because she wet the bed twice (many years after being potty trained) and she was diagnosed with a non-fasting blood sugar of 283. Is he extremely thirsty? Lethargic? Constantly running to the bathroom? Those are some additional signs to watch for.
For now, I suggest testing here and there and keeping a keen eye on him.
As a Type1 I can tell you, after eating a burger my bg would be well in to the 300-400 range. 165 is high, however it is not Type1 high, YET! Monitor him like your Dr. suggested, but dont worry your self sick.
:)