。
I sweated in my armpits.
Literal
Armpit [possessive-の] under [locative-に] sweat [object-を] did.
脇の下 ('under the armpit, armpit') — literally 'under the side'. 汗をかく ('to sweat') is the idiomatic verb phrase, using かく which normally means 'to scratch' but in this idiom means 'to exude (sweat)'. Similar: 恥をかく ('to be embarrassed, expose oneself to shame').