1944, from a specialized use in psychology of German Angst "neurotic fear, anxiety, guilt, remorse," from Old High German angust, from Proto-Germanic *angustu-(source also of Old Frisian ongost, Old High German angust, Middle Dutch ancst "fear," also Old English enge, Old Saxon engi, Gothic aggwus "narrow"), from PIE *anghosti-, suffixed form of root *angh- "tight, painfully constricted, painful." Compare anger.
George Eliot used it (in German) in 1849, and it was popularized in English early 20c. by translation of Freud's work, but as a foreign word until 1940s. Old English had a cognate word, angsumnes "anxiety," but it died out.
Proto-Indo-European root meaning "tight, painfully constricted, painful."
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit amhu- "narrow," amhah "anguish;" Armenian anjuk "narrow;" Lithuanian ankštas "narrow;" Greek ankhein "to squeeze," ankhone "a strangling;" Latin angere "to throttle, torment;" Old Irish cum-ang "straitness, want;" Old English enge "narrow, painful," Old Norse angra "to grieve, vex, distress," Gothic aggwus "narrow."
mid-13c., "hostile attitude, ill will, surliness" (also "distress, suffering; anguish, agony," a sense now obsolete), from Old Norse angr "distress, grief, sorrow, affliction," from Proto-Germanic *angaz (from PIE root *angh- "tight, painfully constricted, painful"). Cognate with German Angst. Sense of "rage, wrath" is early 14c.
From the sense of oppression, or injury, the expression was transferred to the feelings of resentment naturally aroused in the mind of the person aggrieved. In the same way, the word harm signifies injury, damage in English, and resentment, anger, vexation in Swedish.
The idea of injury is very often expressed by the image of pressure, as in the word oppress, or the Fr. grever, to bear heavy on one. [Hensleigh Wedgwood, "A Dictionary of English Etymology," 1859 ]
Old Norse also had angr-gapi "rash, foolish person;" angr-lauss "free from care;" angr-lyndi "sadness, low spirits."