There are, yes. But it is difficult to reliably describe them. The main problem of psychosomatics is poor provability. This "suffers" in general all sciences that study the human psyche. That is, at the level of observation, it can be noted that people whose face is covered with acne most often have psychological problems (as, in principle, overweight people also have them), but it is difficult to objectively prove a causal relationship.
I would use this category as "general well-being of the body." When all is well, it manifests itself at different levels - digestion, sleep, mood. When it is not entirely safe, problems begin at different levels as well. Scandal at work - herpes popped up on the lips. Constant scandals at work - chronic gastritis. Well, and so on. Acne can be associated, for example, with an inability to fend for yourself. It is worth putting the offenders in place - and the acne goes away. How this happens - no one knows. Just like no one understands how the placebo effect works - but this does not stop it working. Maybe scientists of the future will find the answer.
Probably, this is also a rejection of one's own body, its features. Unwillingness to have close confidential contacts with other people. This is all from the experienced rejection by parents or other important people: since they do not need it, then it is bad. And so on. Much has been written about childhood traumas.
Louise Hay seems to believe that acne is a consequence of rejection of one's own appearance. That is, a person is dissatisfied with himself and tries to draw less attention to himself or even "abandon" his own appearance. And the body is one with the soul and mind! So it "adjusts", creating a good reason not to love and hide yourself - acne! An excessive experience of "badness" and "ugliness" is realized.
They are most likely there. In this study by jamanetwork.com, it is said that stress can worsen acne, but why this happens no one knows. My gastritis worsened due to stress, and acne started. Acne and gastritis also added nervousness and a vicious circle turned out.