It's very odd, the way they have treated you, Sammi - they say they are treating you as a type 1 in case (which is good, safer than the other way round) but apart from giving you (inadequate and dated) insulin, they have effectively treated you as a type 2, and a very poorly treated type 2 at that - it's quite common for type 2s to be told "you're diabetic - go away and eat healthily, and come back in 6 months" and not given any more help or information. All diabetics should get more help than that, and type 1s normally do.
Theoretically if you are type 1 you can eat anything you want, though that is assuming that you have adequate insulin and know how to use it. In practice you will find there are things you just can't eat because they send your blood sugar up too fast or send it up so high it takes ages to get down again (this is quite individual, but pizza is a common one), and of course there are things like fruit juice which can only be used as treatment for hypos because they send everyone's blood sugar up fast.
The fact that from the sound of it you already have a healthy, low-sugar diet is another reason for suspecting that you are likely to be type 1. The things you've mentioned eating shouldn't be keeping your blood sugar so high, unless your pancreas is really not working. But it does happen sometimes with type 2, or with other rarer types, so it is sensible that they've done all these tests.
A lot of us have found that medical professionals seem a bit unbalanced in their obsession with hypos! But having said that, while hypos are easy to treat, they are more dangerous in the short term than hypers, so should be taken seriously - if not treated they can kill you very quickly. Highs become dangerous in the longer term, when they are likely to lead to complications. The thing which is worrying us about you is not just how high your blood sugar is going, but all your symptoms which suggest ketoacidosis. So yes, I should keep testing your ketones if I were you, and don't be afraid to keep pestering your doctors about them - it's your health, on the line, not theirs.