I had a very large tumor when I was diagnosed with IBC two years ago. And when I had chemotherapy, this is when the affected breast felt like yours, exactly.
It felt like the tumor was fighting for it's life and moving around and contracting and kicking.
I certainly have no insight into what you are experiencing and have never heard of breast cancer presenting the way that you describe. However, in my humble opinion, any concern about sensations or changes in your breast tissue deserve a visit to the doctor. You are concerned enough to seek out this forum and post, so if nothing else, a medical consultation can put your mind to rest. It can't hurt. God bless...