Rain doesn't cause high chlorine demand, the beginnings of an algae bloom do. I think it's pretty clear that algae's got it's foot in the door and it's time to shock.

As I recall your last reported CYA was 55 - how did you come by that? Half way between 50 and 60? Let's use 60 to be safe.

According to Ben's Best Guess Chart the shock level for your pool's CYA is 20ppm. One large jug (182oz) of plain household beach should get you there to start. Put it in, brush the pool, and test FC and CC half an hour later. Add bleach as needed to get the FC above 20ppm.

As often as possible (at least twice a day): Test FC and CC. Add bleach as needed to get the FC above 20ppm. ( In your pool each Cup of 6% bleach adds 0.7ppm of FC )

Brush the pool daily.

Run pump / filter 24/7; clean as needed.

Continue until one day after you you have 1ppm or less FC loss overnight ( test FC near sundown and again near sunrise ) and there is 0.5ppm or less CC and the water is clear. The one day after is to be sure we've got it all.

You can swim but wear an old suit as swimwear might be damaged by the shock level FC.