I think any time you get symptoms like this it is a good idea to get checked. My thankfully very short journey began with a bit of post-coital bleeding. I convinced myself I had all sorts of other symptoms too, but which most likely were diet/ lifestyle/ age related. Anyway, although I don't have cc I did have CIN3 pre cancerous cells which needed and have now been removed. Not saying you will too, but it is a good idea to get checked, certainly glad I did.
I am sorry that your family has been so blighted by cervical abnormalities. There has not been any genetic link established but it will obviously be a very big concern for you, having seen it first hand several times.
Do go and get a smear, be very specific about your symptoms and if they say it is too soon, politely remind them of your right to a second opinion. You know your body better than anyone.