I've been trying to figure that one out for a while now..
When Esther is being "fitted," she means that she has gone (illegally) to see a doctor to be fitted for a diaphragm, which is a form of birth control that covers the cervix of the woman, preventing sperm from entering it.
I can't seem to find any articles about 1950's diaphragms or why they would cause hemorrhaging. My original guess was that Esther was fitted incorrectly (meaning the doctor failed to give her a diaphragm that fit right), but I'm not sure if that's true. When Esther is taken to the hospital for treatment after hemorrhaging, the doctor examines her and says "You're one in a million," which made me think that perhaps diaphragms in the fifties were capable of producing a rare side effect that causes hemorrhaging.
Then again, perhaps an incorrect fitting was an unusual occurrence as well, making it just as likely. My final guess would be the one stated above: the original doctor that Esther got the diaphragm from failed to give her one that properly fit (possibly one that was too small, given how she bled only after intercourse, and heavily), and the result was that intercourse caused it to either turn sideways or possibly even break apart entirely (considering diaphragms were often made with steel coils and bands encased in rubber).
If the diaphragm were turned sideways somehow before intercourse, then naturally when Irwin first entered Esther, if he did it too harshly (and he might well have, given that Esther was a virgin), then it makes sense that the steel parts in the diaphragm would have been painfully shoved into the vaginal walls or cervix. Then, since Esther decided to grit her teeth and bear it, the repeated entry of intercourse would obviously force the metal parts of the diaphragm deeper into the skin.
That's my best guess, if anyone actually knows for sure please feel free to correct me, because I've been curious about it for years.