I just reread your post and you say that last week you added a quart (4 cups) of bleach and your chlorine went from .5 to >5.5, but from last night with the chlorine at .5 you added 3 cups of bleach and this morning the chlorine was only 1? And the only difference was that you added acid at the same time as the bleach? Unless you have a rather small pool, adding a quart (4 cups) of bleach is not going to have you raise the chlorine by over 5 ppm.

The other posts are correct that adding acid and bleach do not cause a problem unless you mix them together (even pouring them in the same area of the pool) because doing so would be very hazardous as you could produce chlorine gas. Maybe where you poured your acid it migrated over towards the skimmer, but I doubt that. You can always just try adding the chlorine to the skimmer first, wait a few minutes, then add the acid near a return. If this makes a difference, please let us know. That would be interesting!

What kind of chlorine test are you using? Perhaps one of your measurements actually had a lot of chlorine, but was bleached out (this can happen with the DPD test, but not the OTO or FAS-DPD tests).

Richard