You can run your pool successfully with either bleach (or 'liquid chlorine') OR calcium hypochlorite, without draining, and without getting algae.

BUT . . . . to do so you have to move firmly to the BBB method and completely turn your back on pool store chemistry.

To start, read the 'Best Guess Chlorine' page, till you understand it, or at least till you can do what it says. And, order a K2006 test kit, because you cannot maintain the chlorine levels you need, without it. There are links to both the Best Guess page, and to Amazon K2006 ordering, in my signature.

Meanwhile, use bleach or liquid chlorine. To use cal hypo, you'll have to get a calcium hardness test result from the K2006, and tell us what sort of filter you have.