Welcome to TFP! What part of Michigan are you from? Just curious if near Toledo.
Our pool care system and those taught by pool stores do not mix. As such we do not offer advice on whether pool store advice will or will not work. It might, it might not. It might be temporary, might be permanent, we don't know. SLAM works, we see it work a dozen times a week. If you choose to follow the steps given to you by the pool store then it is up to you to decide whether or not it will be effective.
I will say that it is unlikely that your chlorine is too high to swim if algae is living in it. It is also possible that you are not dealing with mustard algae. Without test results (taken by yourself with a proper test kit, not pool store testing or test strips) it is impossible to say on either count.