I forget but you could be cause compression near your trachea or the nerves or muscles near that which if I'm not mistaken can be one of the sx of TOS. The BP is certainly in that vicinity and its offshoots can cause this, I just forget where I read this. Perhaps a google search of TOS and Trachea. or TOS and breathing.

What I suspect is that by practically lying on your front gravity is compressing something to prevent you from breathing. Turn the other way, i.e. on your back, the compression is relieved.