Old English sar "painful, grievous, aching, sad, wounding," influenced in meaning by Old Norse sarr "sore, wounded," from Proto-Germanic *saira- "suffering, sick, ill" (source also of Old Frisian sar "painful," Middle Dutch seer, Dutch zeer "sore, ache," Old High German ser "painful," Gothic sair "pain, sorrow, travail"), from PIE root *sai- (1) "suffering" (source also of Old Irish saeth "pain, sickness").
Adverbial use (as in sore afraid) is from Old English sare but has mostly died out (replaced by sorely), but remains the main meaning of German cognate sehr "very." Slang meaning "angry, irritated" is first recorded 1738.
Old English sar "bodily pain or injury, wound; sickness, disease; state of pain or suffering," from root of sore (adj.). Now restricted to ulcers, boils, blisters. Compare Old Saxon ser "pain, wound," Middle Dutch seer, Dutch zeer, Old High German ser, Old Norse sar, Gothic sair.