Not suprising you are feeling so ill with such high levels....
If I got nowhere with my GP and time restricted with getting an appointment, I have to agree that I would get down to A&E. I would be sneaky and do it in the evening after the suregery is closed, so that I wouldn't be told off by the staff for not going to the GP. Honestly if it was me, I would say that I can't get an appointment with GP, and I feel so ill I have had to come down here to A&E.
They will do the blood tests that you need and give you more time than a 10 minute GP test, you may also get a referral to the diabetic clinic and consultant. You cannot keep going at those levels, that is plain neglect by your healthcare professionals.
My quick test when I was diagnosed showed me as being only 17 (!!!)) and I was immeidately put on to a drip in the hospital and then introduced to the needle regime (type 1).-Along time ago (25 years), and things have certainly changed, but your account is definitely NOT for the better.
I hope that you can find a way to get yourself some help as a priority.