Hi Kate and welcome aboard.
I suspect you already know that the family history and the weight issue both tilt the odds in favour of diabetes. It's not inevitable though and there's a lot you can do to lengthen those odds.
A blood glucose meter would be a great investment. Test your blood glucose 2 hours after meals and you should pretty quickly be able to identify the foods that cause your readings to spike.
If you try and replace those foods with better ones, the meter will thank you and you'll have made a big improvement on your odds.
All the best,
fergus