Do you live with a family or in a school dorm ? Are there other American or International students with whom you attend class ?
Are you saying that your parents will not permit you to shorten your stay to 3 months instead of 6 months ?
Japan should be great because of the culture. I spent 4 months in China & Hong Kong as a college student decades ago. You are in a much better environment from certain perspectives. You need to quit focusing on you. Exercise, read, go out with friends & travel.
P.S. Also do an internet search regarding foods that fight depression.