A neurosis is not a form of mental unbalance. A full-blown mental disorder is called a psychosis, a word built on Greek psyche, spirit, soul, or mind, plus –osis.
A true psychotic has lost contact with reality – at least with reality as most of us perceive it, though no doubt psychotic (note that this word, like neurotic, is both a noun and an adjective) people have their own form of reality.
Built on psyche plus iatreia, medical healing, a psychiatrist, by etymology, is a mind-healer. The speciality is psychiatry; the adjective is psychiatric.
Paediatrics, as you know, is also built on iatreia, as is geriatrics, the speciality dealing with the particular medical needs of the elderly. (This words combines iatreia with Greek geras, old age.)
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