Psychiatry is definitely covered in medical school training (too much, some students say!), as well as other psychosocial aspects of patient care. However, I'd definitely advise against applying to medical school if you don't want to do medicine!
Psychiatrists are doctors. They prescribe medications, sometimes really quite noxious drugs, with very serious side-effects. If you have schizophrenia, you want the person who's giving you the drugs to know the difference between haloperidol, risperidone, and clozapine, how they interact with the body, and what to do if you don't respond to treatment. A medically-trained psychiatrist will also be on the lookout for diabetes caused by your antipsychotic-induced weight gain (sadly very common) or aware that your lingering cough might be caused by lung cancer or smoking-related lung damage (most people with schizophrenia smoke). They also are the ones with responsibility for deciding if you're too unwell to make decisions about your own treatment, 'locking you up' (to put it crudely!) if you pose a threat to yourself or others, and assessing you to see if you might be at risk of killing yourself.
Also remember that the vast majority of mental health care in the UK is delivered by GPs - psychiatrists hardly ever see patients with depression, for example, unless it's very severe, treatment-resistant, and with suicidality. Psychiatrists mostly deal with people who have very serious mental illness.
If you're interested in mental health, but without having to learn about all the body systems, perhaps it might be better for you to think about doing mental health nursing, mental health social work, or clinical psychology?
(I'm applying to med school, but work in a psychiatry-related field)