It doesn't quite sound like Braxton Hicks. Those usually feel like a tightening, but I guess some people do describe them as crampy. Do they come and go or is it constant?
The back pains and tightness in your chest makes me think of gallbladder issues as I had that with my last pregnancy. Again, is it constant? Any rhyme or reason to when it happens? Mine started as random back pain and chest tightness and turned into long, severe episodes mostly in the middle of the night that I eventually ended up at the ER for. Here's hoping it's not that, but it definitely sounds like something you might want to at least call the doctor about?