Have to look for specific doctor, or will a 内科 suffice?

Hey all! I will try to keep this as short as possible:

I have pretty severe periodical insomnia, and have previously been treated with Zorpiclone for it. Despite having lived on and off in Japan for a total of about 2.5 years, not once have I gone to see a doctor. Do I have to look for a specific one, specialising in mental health / sleep disorders, or would going to a 内科 be enough? If it matters, I am located in 新座

Thank you for your time ! Have a fantastic day