DGG has about as much red on it as Hacker News: is it such a heavy use of color? At least on desktop in Safari, the site is pretty 'white', and I'm surprised you get literal physical anxiety.
Interesting! Last time I used the service, about 3-4 months ago, the search results page was awash in red. Now it seems that the style has been much improved to the point of usability. I don't get anxiety like before. FWIW I was/am using Firefox on both Fedora and Windows.
How long has DDG had its current look for you?