There are two types of what they call borderline or prediabetes. Impaired glucose tolerence and impaired fasting glucose. You can have one or the other or both. Often one makes it easier to get the other.
People with an IGF and or IGT have a higher chance of developing T2 in the future than someone without but some never develop T2. There are plenty of long term studies looking at this.
You need to see your hospital notes to confirm if you were diagnosed with T2, sounds like your GP does not think that you were.
If you want to test it is up to you. I have been testing for years but don't discuss it with my healthcare people as they don't like it.
As I get a HBA1C once a year I would have no idea how I'm doing if I did not test. I would also not be able to try and eat foods that don't raise my blood glucose and I would still think porridge is good for me, although needing a nap afterwards is a hint.
It sound like your doctor is saying that you have insulin resistance, are you taking any medication? Your HBA1C at 38 falls into the normal criteria. How do you want your doctor to help you?