I'm a breast Cancer survivor but I don't think you should let them squeeze you so hard you hurt for 2 days afterward. These days my mammograms hardly ever hurt as they have stopped doing what you describe. I think you should tell them about hurting and throwing up your lunch and tell them you'll not continue if they continue to squeeze you so hard. (And, btw, my breast cancer was discovered by a routine mammogram- I had no clue there was a lump there.).
I agree with this. I'm really, really concerned about the lasting damage from squeezing so hard. I just tried to compress my own breasts to 2"...no way in heck can I do it.
You'd think doing that kind of damage repetitively would be a serious contributing factor to issues down the road.
As an aside, I've never had a mammogram. I had a lump in my breast years ago (turned out to be nothing at all) and I requested ultrasound instead of mammogram- my request was granted.