The previous sample tested at 16.5 ppm free chlor.
What test kit are you using to test your shock levels?
Whats your CYA level? ( Pucks will not raise it fast enough IMO. Is a slow process for that size pool)

I would back wash filter, and add DE till the psi goes up a 1 lb.

( A good test to to see if you have a filter issue. Dump DE in the skimmer real fast and look at the return. No white should come out return. If it does that indicates filter issues)

Once filter is running with DE run on high 24/7, Keep at shock level..
Get some clarifier and add that per instructions. 4 oz per 10k gallons I believe.
Get the pink stuff I linked to and add that per instructions.

Post back and let us know what happens in a day or two.

Note::::: Vaccuum and brush the pool after you add the bleach in the evening. Do this every day... I can tell you how many issues are just from not brushing the walls and vacuuming....