I got bitten all over by bugs in the woods.

Literal

Woods [of-の] inside [in-で] lots bugs [by-に] was-bitten.

刺される is the passive of 刺す ('to stab, prick, bite' — used for insect bites). The に marks the agent (insects). いっぱい ('a lot, packed') functions as an adverbial here. Common outdoor complaint.