When I came out of the nightclub

[Bassim]

I am wondering if my sentences sound natural.

When I came out of the noisy nightclub, my head was still throbbing with the deafening music. I took a cab, and when the drive asked me, "Where to?" I replied, "Anywhere away from this terrible racket."

[jutfrank]

We usually say I took a cab when we are referring to a completed journey.

Q: How did you get to the club?
A: I took a cab.

I suggest you change the verb, then, to hailed or flagged down or got in or something else.

[Bassim]

Here is my second try after jutfrank's suggestions:

When I came out of the noisy nightclub, my head was still throbbing with the deafening music. I hailed a cab, and when the driver asked me, "Where to?" I replied, "Anywhere away from this terrible racket."

[jutfrank]

I would say throbbing from the deafening music, to show that the throbbing was caused by the music.

[Bassim]

jutfrank,

I have imagined that the music I listened to was still playing in my head. In that case, could I keep "with the deafening music"?

[jutfrank]

I have imagined that the music I listened to was still playing in my head. In that case, could I keep "with the deafening music"?

Yes.