Hi and Welcome!
Your situation isn't unusual. And the solution isn't tough.
For the moment, concentrate on 3 things:
pH
Chlorine levels
Stabilizer.
What drives me crazy about pool stores is they will tell you to put in a quart of Muriatic Acid, but never even MENTION to you that your stabilizer levels are SO high you won't get your pool clear unless you raise chlorine levels much, MUCH higher.
Our normal recommendation for a CYA /Stabilizer level of 100 is to drain off half your water an refill, which will lower it to 50 and is much easier to manage.
But you CAN clear up a pool with CYA=100--it's just going to take a lot of bleach.
Meantime, put those chlorine tablets away! They are the culprit behind your high CYA levels. Don't use them again, and don't use Di-Chlor powdered chlorine either. And, with your levels of Calcium Hardness, the third dry chlorine option, Cal-Hypo (sold as packets of "shock") isn't a good option either. Only bleach or liquid chlorine will do.
So, here's what I recommend if you cannot drain half the water off and refill.
1) Add 1 CUP (not quart) of muriatic acid to bring down the pH--don't add more till you've re-tested.
2) Add lots of bleach. You need to get your Free Chlorine level to 25ppm! That's right--that's the correct shock level. To do that you'll need to 5 gallons of 6% bleach (if the pool store has 12.5% liquid chlorine add 2 of those instead--same stuff as bleach, stronger concentration.) Since you have a plaster pool, going over the 25 level by a little is no big deal--don't worry about it.
If you DO decide to drain half and refill, then don't add the acid. DO add 2 gallons of 6% bleach.
Retest the water after the refill and we'll go from there.
Meanwhile, we tell EVERYONE this: Go on line and get your own test kit and test your water. The BEST kit is the Taylor K-2006 or K-2006C (larger amounts of test chems) but the Leslies FAS-DPD Chlorine Service Test Kit is just as good as it's a clone of the Taylor kit.
You can get the Taylor kit from Taylortechnologies dot com or amatoind dot com (best pricing). The leslie's kit is available from Lesliespool dot com. You cannot find the K-2006 in stores, though sometimes they have the K-2005--DON'T BUY IT.
You'll pay between $50 and $70 for the kit and it will be the best investment in pool care you ever make. It will pay for itself year after year many times over.
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