I'm really getting irritated.

Literal

Truly prickling-feeling do-[polite].

いらいら is a 擬態語 (state mimetic) evoking prickling, impatient irritation — the feel of restlessness or being on edge. Paired with する, it becomes the standard verb for 'to be irritated / annoyed.' Many Japanese emotional states follow this [mimetic] + する pattern: どきどきする (heart-pounding), わくわくする (excited), うんざりする (fed up). Subject omitted.