If you have a specialized health problem you can visit a specialist ("szakorvos").
As mentioned in the section ‘general health & checkup’, when you feel ill, you should contact your General Practitioner (=GP or “family doctor”). They are familiar with a variety of symptoms, and they can suggest treatment or send you to see a specialist.
Under compulsory health insurance, outpatient specialist (“szakorvos”) care is available on the basis of a social insurance number and with a referral (“beutaló), but for certain statutory benefits, a referral is not required. Specialists are for instance dermotologists, gynaecologists, ear nose laryngologist, ophthalmologist…
You can find hospitals in every district of Budapest, in Hungarian also called SZTK, where you can visit the specialists, you can search online where is the SZTK in your district. Don’t forget to make an appointment online or through phone-call in advance, and be aware that the waitlists can be really long. For all these treatments you need to have a social security code (TAJ).