I have a theory about your headache-inducing car sound: it's your car's fault.
Seriously. Car stereos universally have horrible bass response. It has to do with the intentional manipulation of frequency response by the stereo itself, but mostly it's an acoustical problem. No matter how much money you've spent on aftermarket speakers, it's physically impossible to have flat bass in a car. The volume of air is too small, there are too many resonant cavities, too many reflective surfaces, and too little low-frequency absorption.
But, you say, I have commercial CDs that sound OK in my car. That's because they've been mixed and mastered in a very flat listening environment. Headphones are not flat. Even good ones lie. Even the ones that sound "good".
Especially the ones that sound "good".
Your only hope is to train your ears to mitigate the headphones' defects, and you don't achieve that by listening to your own stuff on them, but by devoting many hours listening to quality commercial references through them. It's not a theory, it's a real psychological phenomenon; over time your subconscious will just know when your mix is right.
If you're using headphones just for mixing in a quiet room (not using them for tracking, not monitoring while a band is playing in the next room, not mixing in bed next to a sleeping spouse) then open-back or semi-open headphones will deliver a much flatter response than closed-back cans.