Should I add pool shock and algaecide at the same time?

No. Pouring pool shock and algaecide in at the same time is a waste of money because the chlorine in shock will break down most algaecides before they can work. Shock the pool first, let chlorine levels drop to normal (24-48 hours), then add algaecide. Honestly, if you keep chlorine at the right level, you probably don’t need algaecide at all.