Tetchy \TECH-ee\ , adjective;
1. Irritable; touchy
This word is first attested in 1592 as teachie by Shakespeare in 'Romeo and Juliet' and before that its origins are unknown. It's probably a slang word, or at least dialectal, and it may have come from Middle English tatch ("a mark, quality") from Vulgar Latin *tecca via Old French. *Tecca was borrowed from a Germanic source related to Old English tacen, which is the forebear of token.
A number of words in English are first attested by Shakespeare, but unlike C.S. Lewis, he probably didn't invent them. I've written about this before, so if you are interested check out my post on slugabed.