'allergically' originates from the English adjective 'allergic' + the adverbial suffix '-ally', where 'allergic' comes from 'allergy' (coined from Greek) and '-ally' is the regular adverb-forming ending in English.

'allergic' developed from the noun 'allergy,' a term coined in 1906 from Neo-Greek 'allergia' (from Greek 'allos' meaning 'other' + 'ergon' meaning 'work'). The adverb 'allergically' is formed in English by adding the suffix '-ally' to 'allergic.'

Initially 'allergy' referred to an altered (different) reaction ('other work'); over time 'allergic' and 'allergically' came to mean 'relating to or caused by an allergy' in modern usage.