If you have a sensitivity to red wine, then no. ANY red wine will affect you.
I speak from experience. In my younger years, I once overindulged on red wine. (I was never so sick in my life.)
It's now more than 30 years later and I STILL cannot drink ANY red wine, no matter how high the quality. I can't even eat food made with red wine, or I'll feel ill all night.
If you're finding that red wine negatively affects you and you want to determine if it's ALL red wine or just "cheap" red wine, then I suggest you order a glass of red wine (good quality, mind you) the next time you're out for the evening.
If you don't get a headache from it, then you've discovered your body just has expensive tastes and you can plan accordingly. If you do, then I think you've discovered you'll become a white wine drinker from hereon out.
To your health!
