You are getting sound advice from us. We've seen LOTS of algae-filled pools and helped clear them up.
Algaecide does no good. Most simply add high amounts of ammonia or copper to your water and make it harder to clear up. The ONLY one we recommend is Polyquat, but more as a preventative. If you add a quart of Polyquat to a 20,000 gallon pool, even with chlorine at shock levels, within 48 hours your chlorine level will be at or near zero. I'm not guessing on this--it's part of my closing routine in the fall. I run my chlorine up to 15 (shock level for my usual CYA leve). I add a full quart of Polyquat (I use about an ounce once a week if at all), wait 48 hours. My chlorine inevitable drops to zero. I then add bleach/liquid chlorine till I'm back at shock level and close.

Other algaecides can cause foaming or gooping up as well.

Add 3 kinds of chlorine, ie LC, Cal-Hypo and Di-Chlor (that granular chlorine you added) does NOTHING more than adding an equivalent amount of bleach. In the water, chlorine is chlorine.

Your pool store guy wants to scare you into buying more stuff. And PhosFree is definitely "stuff". You've heard it here from several people: Phosphates can only feed algae if you HAVE algae. They can't magically produce it.

Carl