It's normal to be in denial and certainly to not yet be convinced. My story three months ago is very similar to your son's.
Like your son, I was admitted into the hospital with a blood sugar of 28+ (the meter didn't read higher than that).
Like your son, I was immediately started on insulin (levemir only and first).
Like your son, I can still look and feel fine if I don't take my insulin(I will explain that later).
HOWEVER....That does not mean nothing is wrong.
Just like
@Type1Bri mentioned, this sounds like the honeymoon phase. There is a HUGE difference between making some insulin and making no insulin. To put that to perspective, I'm currently able to still survive WITHOUT insulin, but it is incredibly difficult (I have to all but remove carbs from my diet).
Long story short and to answer your question: A c-peptide and GAD antibody test usually confirms the diagnosis. Those tests are usually reserved for people who don't know if they have type 1 diabetes or type 2. To be honest, the test that confirms your son has diabetes are the repeated tests over 7 mmol/l (much less 29.5). By definition that is diabetes.
We can't diagnose people on the Internet, but you need to begin coming to terms with the fact that your son probably (almost certainly) has diabetes.
I say that for your sake mentally and for your son's wellbeing. Unfortunately, there are parents who can't accept their children's diagnosis. Some are so far in denial that they have unintentionally put their children's health at risk. I'm not at all suggesting you are guilty of this, but there have been members on this forum who have done exactly that.
-Continue to question what you hear until you get definitive answers. It may not necessarily be what you WANT to hear, but make sure there aren't any doubts.
-Engaging other people with diabetes is incredibly helpful. It's the single most valuable thing I've done in the last 3 months since my T1 diagnosis.
-The miracle treatment for T1 is artificial insulin. HOWEVER, there is no miracle CURE (at least not yet). Please don't start giving your son supplements or experimenting with non-conventional medicine. Unfortunately, I've seen too many parents do that hoping they can cure their children, but ultimately making things worse.
We are all here to help and I wish you and your son the best. Obviously, it's never good news to hear, and it's a scary time for you both I know. However, the way I look at it is this: Good management realistically affects my day-to-day routine, but I do that so it won't effect my life long-term. I want it to be an "Annoyance" rather than let it become something greater.