Yes normally it takes a while to get into ketosis when on a low carb/keto diet. And when you first start it’s easy to be knocked out of it too. So unless you are consistently low carb and have been for a while you more likely are not in nutritional ketosis.
And no, nutritional ketosis does not mean high sugars. The lack of carbs causing ketosis would mean low/normal sugars.
Also colds, flu, rsv, covid and all the other nasty bugs (that on the face of it are quite similar without a test to be sure which it is) will all raise blood glucose in most of us. The immune system in everyone raises bgl to give us energy to fight invaders.
As your diagnosis is still uncertain, and I can definitely understand it’s nothing like a typical type 2 so type 1 really really needs excluding or confirming, keep an eye on both bgl and ketones and seek professional help (111 at least) if they both rise again together. Especially if you feel unwell in any way at all. Best to check than end up in very serious state because you were reluctant to ask.