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@Antje77 says, you could have a different type of diabetes.
What was the reason for being diagnosed as type 2?
There is a common misconception that type 1 is a “childhood disease”. However, more than half of people with type 1 are diagnosed over the age of 20. So age should not be a reason for type 2 diagnosis.
Furthermore, there is a belief you can only have type 1 if it is in you family. Again, this is not true.
I am not saying you definitely have type 1 (I am not a doctor) but, if you do not see improvements with your BG, it could be worth asking to get your type 2 diagnosis confirmed I don’t know how long to suggest but the 6 months of Keto you suggest may be too long if you have been misdiagnosed.
Keep an eye on your BG, fingers crossed for the 6 month remission but if you see your BG continue to climb, revisit your doctor.