Jo,
It will probably help you to consider yourself as T3c, not T2ish. In an earlier post you refer to a Diabetes Nurse, presumably in a Specialist Team and you've had major surgery to your pancreas; so it's more than reasonable to conclude that your diabetes is a result of damage to your pancreas - the classic start point for T3.
The type of diabetes is determined by the cause, not the treatment. T1s have an autoimmune problem that stops them making insulin, they have to inject insulin to manage their BG (Blood Glucose). T2s have substantial resistance to the insulin they are making and thus need medication to assist with BG control; the medication ranges from oral tablets (eg Metformin) to injected Insulin, with options in between. T3s, various flavours from a to h, have physical damage to their pancreas.
If it sounds pedantic to get your condition correctly described, it really isn't. Many T2s are not supported very well because their treatment is, by direction of NICE, covered by GP surgeries where the diabetes expertise is frequently weak. T1s and T3s come under the umbrella of Specialist Teams and can directly seek help from these Teams, including an Endocrinilogist, without GP referral.
With T2 as your categorisation you could be signed off from your Spec Team and put back under your GP, when you appear stable. In the event of being rushed to A& E when you might not be very composed or clear, you might not get the best treatment for your circumstances; the A&E triage might see T2 on your notes and consider that a secondary issue.
I strongly suggest you pester to get your T2 categorisation adjusted to T3c. If your diabetes remains unchanged - then you will be fortunate. But you are taking metformin, which makes an already badly compromised pancreas work harder and there is a realistic prospect of that not being sustainable in the longer term. Diabetes is complicated and confusing; you're probably recognising that from reading threads on this forum. You may need the bigger umbrella of T3c in the future.