An out of whack pool chemical level can cause itching..... combined chloramines, out of range pH are two common reasons.
Just so you know- Algaecide does *not* kill algae. It only helps prevent it assuming your pool is clean and free of algae already. Cheap algaecides also contain copper which is totally unwanted in pools as it can stain the surfaces and discolor hair.
It's far more likely the peroxide is causing the discomfort. I'm afraid a peroxide level capable of keeping a pool clear and somewhat sanitary is also noticeably uncomfortable, it's one of a few reasons we don't promote its use. Most algaecides will not cause discomfort at any level and only some may be uncomfortable but only at extremely high levels that I couldn't imagine you added. Of course, due to the shortcomings with a UV/peroxide system, there is the possibility that something could be growing and causing this discomfort.