Have you had all the diagnostic tests done? If you're getting BGL's in the teens after substantially cutting carbs then there are a number of variables that could be affecting you.
You say you're type 2, although do you know whether or not your pancreas is still producing sufficient insulin? Mine certainly isn't and I have to be on insulin to control my BGLs. The other possibility is that if you've only been diagnosed a short time you may in fact have type 1.5 (aka: LADA) as that is like a slow onset auto immune diabetes and often gets misdiagnosed as type 2. Of course they can find both of the above options out by doing the diagnostic tests again for you.
I hope you're able to get help with getting your BGLs under control. Maybe you need to be on some meds or insulin?
I do know what you mean by depressing.... I get a bit down at times trying to deal with all my health stuff as it has impacted my life in a huge way. I don't care what anyone says about "it could be worse" to me because they're usually not the ones who had to reduce working hours, can't talk properly, can't sleep properly, etc. I try and stay as positive as I can, but I have my moments, days, or even months. I did get told by 2 clinical psychologists that they view I have what they call depression because of circumstances, and not clinical depression because I can still function. They also told me I'm doing remarkably well considering all the stuff I'm dealing with. It is our outlook that matters... each day is a new day to push through and gain what we can.
I wish you the best