Hello JulesB
So sorry you are having a tough time. I think you doctor has given you sound advice considering your family worries, and that you suffer from SAD. Prozac worked well for me at about your age and luckily I only had to take it for a few months, then my moods had balance and I felt normal again.
I would say try the prozac first as not all anxiety and depression is due to the meno. Obviously if it does not help, you and your doctor will have to rethink. HRT works well for some, but it is a long term thing. It would be a shame to start that if a short while on prozac would get you back on track.
Remember, we are not doctors, on the forum, so you must balance whatever advice you get on here with what your doctor advises.
Best of luck