I really feel sorry for you being in such an unconfortable situation with a qatari girl.

You should've avoided it in the first place; or tried to keep her calm at all cost (once you knew her condition).

I'd suggest to patch up with her, if its possible. You can try this, won't hurt anything. simple words of apologies or any kind gestures would push her change her attitude I hope. Then you could start pulling away, while being sympathetic to her situation. Find her something/someone else to play with .. loose here sight/attention/confrontation etc.

some ways to stop humiliating you in public or at work. (you can't keep wearing t-shirt.. saying she's a craxy lunatic)

"Can a person from an big family get you in trouble when you are innocent?" -
Yes, its quite possible. But since you've already spoken well & explained the situation to his father, don't worry nothing will happen.

Police or the Court of first instance, obviously are unaware of her history, so before you could start explaining or bring her family to support you .. you could face lot of trouble with them I guess.

However, believe me you have same rights as a local here.. except the interpretation/implementations can be different. The government authorities will tend to listen to a local first.

hope you'd find peace with this craxy girl.

good luck