Yes it is normal for them to do that. I am 22 and am not where near
menopause or
hysterectomy, but my gyno put me on Lurpron for 6 months after long suffering from pain from my endometriosis. It will put you into a false menopause, but once you discontinue the injections the menopause symptoms will disappear after awhile.
I will warn you, the shots were miserable for me because of the side effects such as nausea, headaches, fatigue, depression, loss of appetite, etc.