You are always complaining about me driving your car.
You are always complaining about I driving your car.
You are always complaining about my driving your car.
There are two options here.
The first guideline is that prepositions take third-person pronouns. So one always complains about me/him/her/them and never about I/she/he/they.
So your second option about I is always wrong.
Many people, unaware of this rule, tend to say things like from my wife and I, which sounds more impressive but is wrong. If you turn the phrase around from I and my wife you see how wrong it is. We don't ever say from I....
But there is another consideration.
Traditionally, possessive adjectives were used before gerunds in the same way that they are still used before nouns.
They don't like my singing/songs
But most native speakers these days say they don't like me singing instead. Most of the time the two constructions amount to the same thing. But there are times when the meaning changes, as in:
They don't like my singing because I'm off key.
They don't like me singing so soon after my throat surgery.
The first refers to the quality of the singing. The second refers to the danger to my health.
In your examples, complaining about me driving is subtly different from complaining about my driving. Whereas the first complaint might concern your age or eye-sight, the second points to your bad driving. But both are idiomatic.
In an English test, I should use my driving.