We can't stop thoughts coming into our heads. We attach feelings to these thoughts depending on our life experience. However we do have control over what we do about these thoughts. We don't have to chase them and we certainly don't have to act on them if they they are harmful thoughts. We all live in our heads, but what we think is not necessarily real. For example, I used to worry what other people think about me, but in reality they were unlikely to be judging me. They were too busy with their own concerns. I know someone who has had a successful life and is generally happy, but still has suicidal thoughts. He has learnt, with support, that that is ok as thoughts pass, along with any attached thoughts. He doesn't act on them.
I do urge you to seek either counselling or life coaching, as long as you choose someone you feel comfortable with. I have found this support invaluable. CLKD's suggestion of seeing a doctor first is a good idea, particularly if your husband is prepared to come with you.
Hormones do have an effect on our emotions, but our life experience does have a huge bearing on this as well. It is too simplistic to blame this on the menopause.
Have you had a family of your own? Many mothers have experienced feelings akin to bereavement when their children leave home. They have the choice to deal with how they feel or become needy with their children.
You have had a very intense experience helping this young lady for a relatively short period of time. Your feelings were intense as well and now she has left, you are left high and dry. I may have sounded unsympathetic. I am sorry for how you feel, but I cannot condone you acting on them. You are important and you deserve support, but so does this young vulnerable woman. I hope she has support from others. I wish you well.