Your pump is the most massively oversized pump, compared to the filter, I can remember encountering. A 1 HP AG pool pump is too large for a 100# sand filter! If it's really a 2HP pump, it would blow the algae right through the filter.

+ There's no answer to 'how high can you go without bleaching the liner'. I'm not sure if the liner makers know, but I am sure that if they do know, they're not saying! I can tell you it varies from maker to maker and liner to liner (within a single brand) and even from year to year, as the printing dyes vary. Reported, dark blue is the most susceptible color.

You need to post current test results, especially including CYA levels.

+ Once you work out a dose, you need to (a) put the pump on recirculate, (b) begin repeated doses of chlorine till it's ALL dead, (c) brush the heck out of the pool to stir up any remaining live algae, and then (d) let it settle and vac to waste.

+ You really also need to step down your pump. It's possible in many cases to put a 1HP impeller in a 2HP pump, and that would help, a lot. Also, most of the sand in your filter has probably been lost while backwashing, so you'll need to check that.

Good luck.