Hmmm, so, you're taking 6U of Novolog regardless of what you eat? If you decide to start low-carbing again, make sure you test your BG frequently. Lows sucks!
I just thought of another question: have you ever tested for ketones? With a BG of 280 mg/dl or higher, it is possible that you'd spill ketones (if you're a T1). I don't think T2s spill ketones, except in rare cases. Also, have you had any unexplained weight loss? These are common T1 signs.
But, to answer your question, yes, it sounds like you could be a "double diabetic." I think it is common for T1s to experience some insulin resistance through weight gain, so depending on your current weight, you might find that the resistance gets better with weight loss.
As for going on insulin, I was devastated at first. I was a complete needle-phobe before, and always considered T1 diabetes to be "the worst thing that could happen to me." Now, over 10 years later, I've gotten very used to it all. It still sucks, no doubt, but it's livable (and it beats the alternative)! If you do end up on insulin, I highly recommend getting a pump and CGM. They've helped me get my A1c down to the low 6s (possibly even lower - getting bloodwork next week).
What kind of healthcare provider are you? I've always heard that you guys make the worst patients
I'm always happy to help! Please keep us posted on your status - I'll be interested to read what your results show.