When I have an exceptional amount of pain my kids comment how pale I look, they know I don't feel well. I think that is a common symptom with pain, however I am not sure. Also I have Iron deficiency anemia, which I am sure many of us have possibly from malnutrition? That can cause you to look a bit pale I believe.

I think the stress of severe pain causes pallor- less blood flow to skin.

That makes sense, this gives a good explanation also: https://www.healthline.com/health/mottled-skin