What can I do about bright red and hot ears?

It does sound like an allergic response. Other causes are menopause, too much caffeine, high bp (uncommon) and a few rare things.

Here is one of many sites red hot ears

My face use to turn red and hot when I ate chocolate cake. It was temporary, and now that I no longer eat chocolate cake, my face stays cool and dry (unless it is 90˚).

Treatment is draconian (beta blockers). If it is just every so often, use the ice or live with it.

I just wash with water and apply benedryl ointment. That always works for me.
Just notice you have eczema. Maybe your shampoo or soap is the problem.

Try some aloe gel. Store it in the fridge when you are not using it.

I have on and off Raynaud’s Phenomenon. I’ve had my fingers, toes, ears and nose go bright red at times. I just wait it out.