I am 24 or 25 weeks and have just started having the sternum pain that you are talking about (in addition to all the other pains and heartburn that you mentioned). During my first twin pregnancy, I did experience the horrible heartburn, the sciatic pain (which did not go away after birth for me until I started with a chiro) and pubic symphysis pain. But, I never experienced the sternum pain until this past week. I don't know why it's happening but I just figured it was something else that happens sometimes during pregnancy.
Sorry I'm not too helpful but I thought I just let you know you are not the only one!