Leslie's Chlor-Brite is Dichlor and is the most irresponsible pool product sold as a "shock" (which is really a verb, not a noun) that is on the market. The reason is that with Dichlor, for every 10 ppm Free Chlorine (FC) that it adds, it also increases Cyanuric Acid (CYA) by 9 ppm. If you've added a lot of this to your pool, then you've increased the CYA level as well which makes chlorine less effective so requires even higher FC levels to kill algae.

I would not trust the pool store numbers, especially not for CYA. You really need to get yourself a good test kit: either the Taylor K-2006 you can get at a good online price here or the TF-100 from tftestkits.net here with the latter kit having more volume of reagents so is comparably priced per test. You can compare these two test kits in this post.

If your pool was "let go" over the winter and the chlorine got to zero, then bacteria may have converted some of the CYA into ammonia. So your chlorine demand may be huge. Though any oxidizer could get rid of this, bleach or chlorinating liquid is usually the least expensive way to go -- non-chlorine shock is usually 3 times as expensive.

If you want to get an estimate of how much chlorine it might take, do a bucket test by taking a 2-gallon bucket of pool water and add 6% bleach to it noting that every 1/4 teaspoon of 6% bleach in 2 gallons is 10 ppm FC. Add some bleach, wait an hour, measure the FC. If it's not holding (i.e. much less than 10 ppm FC) then add more, wait an hour, remeasure. Once the FC holds then that cumulative amount of FC is what will be needed for your pool -- it could be a lot.

Richard