Any hypochlorite source of chlorine (bleach, chlorinating liquid, Cal-Hypo, lithium hypochlorite) will have the pH rise when you add it to the water. It is when the chlorine gets consumed/used that the pH drops back down since that process is acidic. The pH neutrality comes from the combination of chlorine addition AND consumption when you end up back to the FC where you started. As I noted, there is a small net pH increase from all of this, but it is usually relatively small compared to the pH rise from the outgassing of carbon dioxide caused by the TA being too high or having more aeration.
As waterbear noted, you need to deal with your algae problem first. As for test kits, get the Taylor K-2006.
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