For about a year, I had a pain that sounds sort of similar, on the left side, rising up until it was under my breast / nearish my sternum, got worse at night, bad enough so I felt as if it was making me sometimes catch my breath. I thought it was something to do with my heart and did go to the doctors. From memory, I think they said it might have been acid or reflux or stress or something - basically, nothing to worry about, watch and wait. Anyway, round about the same time I started have regular massages (every 3-4 months); and she said it was because I'd become so right dominant (desk job using a computer 'mouse stretch'). After a couple of sessions with her, it disappeared and has never come back. I also changed jobs, so don't sit at a computer anymore.
My memory is pretty shonky, so don't take this as gospel, but I also think it started happening at around the time I began HRT and went when I stopped about nine months later. However, I don't believe HRT was the cause, instead, there was just so much going on with me back then that I'm pretty sure I was holding my whole body in some sort of tension permanently.
Hope you get it sorted.