Your dermatologist doesn't know any better than you in this case, though I think he's wrong to be dismissive.
This stuff about the gut-skin axis has only been coming out the last 2-3 years, although there are a few lone researchers who have been thinking this for decades.
For myself, I experienced roughly 80% reduction in symptoms after switching to a strict vegetarian diet two years ago, and it's stayed that way.
You might want to look into trying an elimination diet. There are quite a few resources online for this and gist of it is that you cut out a whole bunch of food types that have been known to cause issues with some people. After a few weeks of that you add back in a single group of food every few days and check if any symptoms return.
Some people have had luck using this method to find issues that doctor visits weren't able to surface.
Eventually I went back to just eating regular food and within a month it was coming back along with not feeling as great.
I have still never been able to nail it down, and my dermatologist is pretty dismissive of it.