Hello Bayadere,
You may have been looking at the Ketones page for that advice, however the advice is to call a Dr only if he has two readings above 13.3 AND there are ketones present. As Ken correctly says, you must get hold of some Ketostix. Your son is now entitled to free prescriptions for everything for life however I'd suggest you just go and buy a bottle for the minute to save all the hassle and get them into the house. The reading of 14 will (again, as Ken said) be related to his food. Have a read of the ketones page again to be sure you understand. Yes in general highs aren't good but neither are lots of high-low swings. They will build up problems over time. Equally, bringing his sugar levels down too quickly is dangerous. So, just stick to what you've been told to do for now, get some ketone testing strips to be on the safe side, and go to A+E if they are +2 or above (that's the advice I was given when newly diagnosed just over 2yrs ago). Call a Dr for advice if there are traces or they're +1. Bear in mind that lots of people get 'starvation ketones' which is when you haven't eaten for several hours, and that's completely normal and not to be fretted over - they'll disappear when you eat. Any time there are ketones, drinking water (sipping 100mls every hour or so) will help to physically flush them out of your body and that's a step you can take without any medical advice!
Hopefully your son is going to be able to get onto what's called a DAFNE course - it means "Dose Adjustment For Normal Eating" - and then he'll learn how to take total control over his insulin/food intake and he will then be given slightly different levels to aim for than the ones Ken has given. I would add here that the best practice is to be 5.5 or above on waking as 4 is very close to hypo and the current advice from DAFNE is that is too low to be waking up on as it could signal he's been hypo in his sleep; if he's regularly in the 4s on waking, please mention it to the Dr/diabetes nurse (but don't be overly alarmed). They will either slightly reduce his background insulin or slightly reduce the dose of the last meal before bed. That should sort it out. Only do what they tell you for now - don't make any decisions on your own unless they give you some scope to do so - there are many things you don't yet know and playing with it could be playing with fire until you are all better informed.
The key for the moment is don't panic. Treat hypos seriously and immediately, and test for ketones when ill and/or repeatedly high, but otherwise just continue. If he is getting highs all the time but he's not ill and there are no ketones then the hospital will alter his doses. Keep in contact with them. One thing to watch out for is he is a candidate for something called the honeymoon period - this is when the body weirdly decides to make its own insulin again (they don't know why) and it happens after you start injecting. It can go on for up to a year or so, as it did with me, and then the doses will have to be drastically cut. So testing on waking, before each meal and before bed is key. If worried about overnight levels, test at 3am as this is when the body will normally go low anyway (even in non-diabetics). The best advice for type 1s is not to test after meals unless you feel funny, but if you do, being under 9 is good (but not too low, as the insulin is still working after 4-5hrs, even up to 6hrs sometimes). I have to say that if I'm under 9 2hrs after injecting, I can easily slip into hypo territory so, of course, everyone is different. I definitely prefer to see a 10 or so, 2hrs after food, but that's come with personal experience and it isn't the same for everyone. It's going to take quite a long time to stabilise and get used to everything so don't worry it will all become clear over time. You can find more advice on the Type 1 section of this forum. Your son is lucky to have someone close to him take such an interest in how this all works - none of my family have a clue and they haven't even asked.
Best of luck.
Moonstone.