Firstly, hi and welcome
@autumnsavannah - take a breath and relax: everything is okay.
Sugar and ketones could be present for any number of reasons (though they sure are odd assuming your son is eating a typical diet for a child his age - fruit, potatoes, pasta, veggies - but, still, you said he was unwell and something a simple as a UTI could cause those results.
High blood sugar is also normal when someone is unwell, dehydrated or otherwise experiencing discomfort, and that result also could have been affected by how long it had been since breakfast, how frightened he might have been to be in hospital, whether you gave him a drink while you were waiting... all kinds of things. It dropped, and that's great news.
It sounds like you have an attentive and proactive team who have equipped you with the main thing you need for the time being, but, perhaps, not quite explained its purpose to you.
Firstly, that meter isn't perfectly accurate - it gives a very general idea to an accuracy of +/- 15%. Also, unless you pair the readings with what your son eats, the data isn't going to be much use beyond demonstrating that he spikes after meals and then drops again after some time has passed - and we all do that.
When I'd recommend is keeping a rough log of what he eats and drinks alongside the meter readings. That way you and your team can see how he's responding to particular types of food. But, also, take a reading just before he starts eating and then note how long it's been since he last ate when you test again.
You've got a date for a more formal blood test: if they were very concerned, they'd have done that in hospital. At the moment, they just want him well (because infections and whatnot will mess with his BG levels).
It's hard to say to a parent "Don't worry too much", because good parents worry constantly. But, honestly, your medical team seem to be moving with deliberation and caution, which isn't how things go when there's an emergency. Get him well again, do his bloods and try not to stress in the meantime as he'll pick up on your anxiety.
Honestly, if he
does end up with a diagnosis of diabetes, it's far from the end of the world. You'll be amazed how well you'll learn to cope with this and there's oodles of support from other families in a similar position available on these boards:
https://www.diabetes.co.uk/forum/category/parents.16/
Hang in there: I know it's rough and a real shock, but, believe me, you'll feel much better when he's at least up and about making mischief again. Everything after that, you'll learn to manage. Promise.
Keep in touch and much love to you,
Sock xx