I agree with ruddyduck. I shot fixed blade thunderheads for 5 years with no issues. Took shots out to 40 yards and my arrows flew as true as I could have possibly wanted.

Ironically enough, switched over to mechanicals this year (just to try something new) and had the EXACT same thing happen to me as you. Had a doe at 35 yards, looked like a clear shot, arrow was headed right for the vitals - and right before impact took a sharp turn to the right (just missing her throat as well...kinda crazy). Luckily it was a clean miss. But anyway, turned out there was a thin twig that I could not see from where I was about 5 yards in front of where she was standing. Very frustrating, especially since I need to fill my doe tag and I am 0 for 1. So in summary, IMO i dont think it was the bloodhead.