If this were true, we would expect that other things that decrease blood flow in the face (such as cold weather, maybe?) would also increase acne.

Cold weather might reduce your blood flow for a few hours but it will come back to normal once you are again in a warm environment.

If I would run an experiment I would attempt to measure how tense the muscles in the face happen to be and how warm the skin happens to be and see whether those ratings correlates with the amount of acne.

This is very interesting; is this a significant cause of acne, and if so how do you know?

It's a working theory of myself at the moment.

The background is there are techniques in the hypnosis realm for resolving "trapped emotions" which often work to help solve physical alignments.

My perception of the bodies of other people is also getting better and I get better at perceiving when a certain part of the person I'm interacting with is colder and tenser than it should be.

Acne is caused by excessive face-washing, which screws up homeostatic processes controlling the amount of oil and water on the face.

As far as self reports go, some people improve their acne by washing their faces less and others by washing it more.

Acne is a defense mechanism employed when the body detects that one is low-status. That is, it's a way of making yourself less threatening to the rest of the tribe so that they won't slaughter you. If true, this could be mediated by status hormones like testosterone and cortisol.

Hunter gatherer tribes have nearly no acne. I would be wary with an explanation that focuses on the utility of getting acne in a hunter gather tribe to explain the acne we have in Western civilisation.