Perhaps it is caused by lying on your left side? You said it happens under your left breast when you lie on your left side, maybe it's a nerve twitching?? Kinda like if you sit on your foot for too long and you get pins and needles .... it's just a suggestion, but maybe a nerve is being pinched causing the vibrating sensation?

ETA: And it might be a good idea to ask at your ante natal classes - the midwives may just have the answer!