Some researchers estimate that as many as 70 percent of women suffer depression after hysterectomy. While the depression might be shortlived for some, for others it can become chronic.
The abrupt hormonal changes caused by the surgery affect the nerve and neuroendocrine interactions which may result in a loss of any sense of emotional well-being, and can cause mood changes and irritability.
While your sister may have understood that there were sound medical reasons for surgery, and gave her consent to the op, she may have grieved for the loss of her womb and may feel that she is not a 'complete' woman. This will, understandably, compound her depression.
I'm not sure what you mean by 'a daily support thing' or why your sister's GP cannot prescribe diazepam or other medication until it is put in place but if your sister is now being perceived as being, or is being treated, as an alcoholic, her medical history needs to be urgenty reviewed so that she can be prescribed appropriate drug regime.
Your post has made me feel extremely angry on behalf of your sister and her family (including yourself, of course) as, given appropriate treatment (which may include HRT, anti-depressants, and counselling), there was, and is, no need for her to suffer the crippling effects of preventable or manageable post-hysterectomy depresssion.
It would seem that your sister has been failed by the NHS and has been left to self-medicate with alcohol. If I were you, I'd be giving her GP hell insistent that your sister needs a hormonal evaluation NOW and a course of an appropriate anti-depressant pending the results.
If you can't achieve this in the next week or so, and if your sister functions 'normally' with low doses of her drug of choice, I suggest you do what's necessary to get her off the sauce.