Hey Bumpy -
So sorry for what you're going through with your voice
I had a TT in 2008. They also "sacrificed" as they call it, the right laryngeal nerve, as the cancer had encased the nerve
So I have a permanently paralyzed vocal cord. I had almost no voice after my surgery, and it took several months, probably up to a year, before my voice really improved. I have been very fortunate to regain most of my voice. Many others are not so lucky.
Your situation is different though, as you still have the laryngeal nerve intact. My very UN medical opinion is it's due to trauma, and hopefully you will have a full recovery of your voice in time. Isn't it a strange feeling though?? Try not to strain your voice too much. You could do damage if you strain it too much this early on. Reece is correct - speech therapy can do wonders, but if I were you I would give it some time