Did you not wear your strap diligently?

I've broken both clavicles, one when I was too young to remember, the second when I was a freshman in high school (2001). I had a strap that I wore, probably similar to yours. Yea, it wasn't comfortable, but it worked. I couldn't lift my arm above shoulder height, so I had to wear button up shirts instead of t-shirts. If I remember correctly, it was 4-6 weeks or so for it to fully heal, but I was a kid then. I would expect it to take longer now.

Neither of my breaks healed 100% perfect, I can feel bumps where the bones didn't meet up exactly, but I don't think they're anywhere near as bad as yours. I would definitely listen to the doctor or try to get a second medical opinion. As another poster stated, I wouldn't take medical advice from random strangers on the internet, even those who have broken a clavicle (or two!).