Find a different doc. Although you are young this pain is taking over your life. It should end whether that means a hysterectomy or some other form of surgery.
I took Danacrin for my edometriosis. That was back in the 80's though. It is a male.....medication. It stops your periods while you take it and it gives your body a pelvic rest.
Since the uterus is not making the lining there are no cells to go to other parts of the body. The ones outside the uterus dry up and flake off. It basically clears up all the out of uterus growths if you take it several months in a row. This type of med should clear up the issues.
Once you stop taking the med though the lining of the uterus will start flowing and those cells will find the place they are getting out and go back and start the whole process over again. This is why a hysterectomy is often the only "cure" for this disease.
There were a lot of "stories" of how the cells got outside the uterus. The one I remember is sex during your period.
When a woman climaxes she bears down. The uterus contracts and if there is tissue/blood/stuff (On her period) in the uterus it has to go somewhere so it backwashes out the tubes into the abdominal cavity where it moves around and can eventually go to any spot in the body. Each month it gets triggered by the hormones and becomes it's own little uterus.
It sloughs off cells that move around and find someplace to attach to and the attached bits grow and cycle each following month, sending out more to do the same thing. So it never ends until the woman's hormones signal the end of menses.
I found a specialist that did a lot of work with this disease. Most women who have any signs of endometriosis are sterile. So it's odd that your doc won't do a hysterectomy.
The uterus, tubes, ovaries, all the surrounding organs and tissue get scars on them from the little fake uterus's as they grow, expand and contract each month. The uterus and other organs become stiffer with all the scars from the tissue adhering to the outside of it, the scar tissues don't stretch, they don't move the same way. SO if a pregnancy does start it usually can't grow beyond a certain point because the tissue can't move.
So I find it odd that a doc would not give a thought to hysterectomy in this instance.
If you find a doc who is a specialist in this illness I think you'll find a different style of treating it. You could do the male hormone, do some more removal of tissues, all kinds of stuff.
I do think giving the therapy a go would not hurt. You will learn something from it even if it doesn't help your symptoms.