Rash from crying

Is this normal? My baby is fair skinned and whenever she cries for more than a couple seconds she begins to break out in a rash. The skin on her cheeks, nose, and eyebrows gets very red and she gets tiny red dots (not raised) on her forehead and the sides of her head and chin. Once she calms down they fade within 10 minutes or so. I assume it’s because she works herself up?