Anytime your child seems off or overly emotional, test. As a kid I remember getting so busy playing that I wouldn't notice I'd gone low (kind of like how little kids wet their pants because they they're having too much fun to stop and use the bathroom).
It's not unusual to be 50 or much lower and still function just fine. And the more lows a diabetic has, the more comfortable the body feels when it's low.
The good thing is that because your child is a new diabetic his body still releases adrenalin when blood sugar drops. That causes the physical symptoms like shaking and sweating. The bad news is that because the brain doesn't have enough glucose, a low makes the diabetic dopey, and they are like a drunk person whose brain is impaired.
THAT'S what's frustrating about lows... right when you need to help yourself the most, your brain stops working. It used to drive me crazy that my mom, and later my husband, can tell that I'm low before I sometimes can. But I've learned to just appreciate having people who love me. My husband and I made an agreement that even if I know I'm fine, I will test anytime he asks me to.
You may read about hypoglycemia unawareness, where the diabetic doesn't have any physical symptoms of a low. That isn't usually an issue for diabetics until they've had the disease at least 10 years. Having lots of highs and lows will make a person prone to hypo unawareness because after years of having lows all the time the body doesn't set off alarm bells (and release adrenalin) when blood sugar drops.
Even if your son does develop this at some point down the road, know that hypo unawarness can be reversed. Mine went away when I got an insulin pump and was able to prevent a lot of extreme highs and lows. Now I can feel when my blood sugar hits around 70 and have low symptoms when I drop lower than that. To be safe, I still make sure to test before I drive and when my son was an infant and I was home with him, I tested every couple hours to be sure a low didn't sneak up on me.
Don't fear lows, just have a healthy respect for them. They're a part of life with diabetes because it only takes a little extra insulin to cause one. Your son and your family will figure out how to identify and deal with lows. Take care.