Don't add any algaecide in the meantime. Most make more of a mess than they do anything good.

Shocking once may or may not kill algae, but, maintaining sustained high cl levels will -- if you maintain it high enough to compensate for whatever your cya level is. That is why we need a complete set of current water testing results taken with a drops based kit - no teststrips.

But, ultimately, yes- shocking will kill algae and then you have to be sure to maintain proper chlorine levels to keep it from coming back.