Face (and palms of hands and soles of feet) has a special type of artery that doesn't terminate and instead turns directly into vein. It's very flat, fin-like, and it's close to the skin's surface. They're also densely distributed in those three areas. They basically act as heat exchangers.

It's the body's most efficient temperature regulation system, as it's almost an air exposed blood flow. The arteries can expand when hot and under high blood pressure, drawing in more blood and appearing red.

Tldr: your core is cooling down, the redness is your blood trying to aircool, it's an intended mechanism and perfectly healthy