I didn't notice a mosquito was biting my arm.

Literal

Arm [object-を] mosquito [locative-に] being-bitten-[state-ている] [possessive-の] [locative-に] did-not-notice.

An observation about inattention. 蚊 (か) is 'mosquito'. 刺す ('to sting, pierce') is the verb for insect bites — so 刺される is 'to be bitten by' an insect. Japanese uses 'sting' (刺す) rather than 'bite' (噛む) for mosquitoes — an interesting conceptual distinction. The whole '~に気づかない' ('not notice') takes a noun or nominalized clause.