No need to precisely distinguish Psychiatry from Psychosomatic Medicine — many clinics offer both together; either is fine, the doctor will determine the direction after talking with you
You can first consult Psychiatry/Psychosomatic Medicine; Japan has government-designated "Addiction Treatment Centers" in each prefecture that specialize in alcohol/drug dependency, though not every psychiatry clinic has this — you can search for one near you via the Kurihama Medical Center website
This is a typical early sign of dependency — be honest with your doctor, there's no need to feel ashamed. Japan has government-designated addiction treatment centers that handle this more specifically than general psychiatry
If you have thoughts of suicide or self-harm, call emergency services or go to an ER with psychiatric care immediately, or call a mental health crisis hotline