Hello,
Firstly, stay calm

If you do have diabetes, stress can make it much worse!
You've correctly identified many common symptoms...frequent urination and thirst are very common (although not specifically at night). Family history also increases your chances of developing type II.
If you are worried, definetely go to your Dr and get tested again. Preferably, ask them to do a blood test...they'll probably be able to do one right there with a blood glucose monitor in a matter of seconds. It'll take a few tests, including a fasting blood test, before they confirm a diabetes diagnosis, though. So again, stay calm. Chances are, if you have diabetes, you've probably had it for at least a few months.
Finally, don't be scared. Diabetes is a serious condition but it's managable. I was diagnosed early October (my blood glucose level was 16!) and already I have my blood sugars under control with a low GI diet, exercise and small doses of Metformin. Now my glucose levels are at a perfectly respectable 4-6 ish. Since I've gotten my blood sugar under control I feel SO much better! My acne is slowly clearing up, I have SO much more energy and I really respect what I put into my body! I'm losing weight because my diet is better, although I feel like I'm eating tonnes- obviously it's a real incentive to watch what you eat! Also: don't think Diabetes means you wont be able to eat any sugar or anything. I quite regularly eat a little dark chocolate, plenty of fruit and other occaisional sweet treats. I'm much more organized because I *have* to be.
My point being: Diabetes has been something of a blessing in disguise for me! I hope everything works out for you!