Hi, and welcome to the forum!!
With the weather this hot (I'm near Shreveport, LA, so I have basically the same climate as you), it won't take much at all for an algae bloom to get started, and if you've spent any time at all with a CYA of 120 and chlorine less than 8 ppm, you probably are losing most of your chlorine to an impending algae outbreak. You need to stop using the trichlor tabs at this point, and go strictly to non-stabilized chlorine (bleach!), otherwise your CYA levels are going to keep rising. See the "best guess chlorine chart" linked in my sig for more information on where your shock level and regular chlorination levels need to be with a CYA that high. Also, the trichlor is what is driving your pH down--once you stop using the trichlor, you shouldn't have any problems keeping it above 7.2 just by pointing your return jets upward so they ripple the water.
You need to shock your pool up to 25 ppm, and hold it there by testing and adding whatever chlorine is needed to get back above 25 ppm, until you can go from sundown one night to just before the sun hits the pool the next morning, and lose 1 ppm or less of chlorine. At that point you can let it drift back down, but with a CYa that high, never let it get below 8 ppm.
Running a high CYA pool is not necessarily a bad thing, and it's about the only way to manage a pool without losing too much chlorine to the sun. I purposely run mine at 80-90 ppm because I lose less chlorine daily there than at lower CYA levels, and it allows me to dose evern 2-3 days instead of every day. So a CYA of 120 is not necessarily "unacceptable", and I would have no problem with running it just the way it is--you just have to get rid of that chlorine demand by shocking. No more trichlor tabs!!
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