I changed my diet in late may as I was carrying too much weight, and to help with the glucose intolerance.
Okay, well correct me if I am thinking about this wrong, but the 12.8 occurred after you started cutting calories, right? That means your baseline could be above 12.8.
I should add that you can't really go by one reading. Testosterone does vary quite a bit and I sometimes think the labs aren't perfect either.
I feel I have always had low levels, and have recently found out that my father also suffers from low libido. Is it hereditary???
Testosterone is a huge factor in libido as you probably know from personal research and poking around my site. But it is certainly not the only factor. Almost any weak link in your personal health can affect it significantly, including immune-issues, poor nutrition, sleep disorders, stress, thyroid function, Vitamin D, being overweight, depression, medications and on and on.
I am not saying those apply to you. But I'm saying you have to start digging one-by-one and steadily working on your health. Your body is essentially a very complex race car and you have to learn how to manage it and understand it as best you can. Get good docs and medical experts to help you and read a ton as the docs are certainly not always perfect as you can tell from poking around this forum!
So, to answer your questions:
1. Your low testosterone may be related to a) a reduction in calories from dieting and b) being overweight. This may substantially improve over time as you lose weight and then restore baseline calorie levels. There is no way to know for sure except to try it.
2. It is almost for sure not heriditary. Many, many studies have examined native peoples who live disease free (from all our chronic conditions) but then begin to live a Western lifestyle and their health starts to rapidly degenerate. It could be some weird mutation, but studies show that it is unlikely.
3. Your libido is undoubtedly being affected by your lowish testosterone but could be affected by many other factors as well. Start building up your general health and libido will follow: it's another great barometer (like erections) of overall health and well-being.