Re: Wow, there's so much I don't know about hair!
Hair growth is indeed very often ethnic and tends to run in families. So if your mother and grandmother had significant beard growth, then it would not be surprising if you did too. A very large number of women do have "male pattern" beard growth.
Being on the pill has unpredictable results for hair growth while you're actually taking it. It often reduces male-pattern hair growth while you're taking it, because it increases your estrogen levels. However estrogen from the pill doesn't always have quite the same effect as your own natural estrogen, and does have the effect of shutting down your natural estrogen production with the result that when you come off the pill you will have little or no estrogen of your own and you body may be slow to restart production, if it does so at all.
The story about shaving causing the growth to be faster, coarser etc. is entirely a myth. What is certainly true is that most women start shaving BECAUSE their hair is already getting coarser and more abundant and then when the process of getting coarser and more abundant continues, they go and blame it on the shaving, whereas all that has happened is that what had already started has continued. Of course it always feels a little bit more stubbly if you cut across a hair, but all you've done is cut off the fine end. The bit you've cut is no thicker than it was before you cut it.
If your mother and grandmother had beard growth, do you really need to go to a doctor at all? I would have thought that the simple answer is to recognize it for what it is -- simply a fact that in your family it is common for women to have beard growth and to treat it accordingly -- get a proper electric razor -- try a Norelco from the men's range (they're called Philishave everywhere else in the world outside the US) and shave as often as may be necessary. End of problem.