I should take your fasting BG several times in one day, and see how much it varies over time. Then do it again on another day. You might be surprised by the results.
I have noticed that my surgery seems to treat my fasting BG as some sort of immovable, absolute diagnostic tool. Like some sort of magic number. However a little home experimentation has proved this to be absolute nonsense (in my case),
My fasting BG will vary from 5.8 on waking, up to 8.5 just before breakfast. Add in factors like lack of sleep, what I ate and exercised the day before, and what time I eat that breakfast... it turns out that my fasting BG is highly variable and useless for the purpose of diagnosing diabetes!
But they still want to treat it like an absolute...
So yes, an OGTT or an HbA1c will be more use - unless you low carb, which messes the results up a bit too...