Hot face?

So over the past few months my cheeks and ears have been getting really red/flushed and hot and I'm pretty sure it's down to eczema because when I put cream on it it stings a bit. But does this happen to anyone else? How can I cool them down because Ice or any cold compress only works while its actually on my face, the minute I take it off its red hot again.

It's not the worst problem in the world but its kind of embarrassing when my face goes so red so often because it looks like I'm just blushing real bad. And it's so uncomfortable when it gets really hot.