You should most definitely order the Taylor K-2006 kit you can get at a good online price here. You'll want to test your CYA level as well as the other levels. Any pool store test, especially for CYA, is essentially useless -- they are almost always wrong. In the meantime, why don't you do the bucket test I described to get an estimate of how much chlorine it's going to take to clear your pool.

If your CYA level is through the roof, then you'll need to do at least some partial drain/refill. If it's not, then it may just take a lot of chlorine which the bucket test will tell you.

As for whether you want to continue to add chlorine in the morning, that's up to you. Basically, you only have two choices -- add a lot of chlorine or dilute the water. Any other oxidizer other than chlorinating liquid or bleach is going to cost you more. Dilution will cost you the water and sewer costs though even a partial dilution could be helpful -- it depends on chlorine vs. water/sewer costs. A bucket test will at least give you an idea of how much chlorine you'll need.