If the black spots are algae, and you are having trouble getting rid of them, then you should bring your FC levels up to shock level, which for you is 20+, and keep it there while you brush and test daily until the algae is gone. You would then do an overnight test and if you lose no more than 1 ppm chlorine, you can let your chlorine levels drop to 5-10 ppm.

Do you have a reading for CC? If its 1 or more you need to shock. Interestingly I have found that even with a CC of 0.5 or less, if the pool looks like it has algae, it probably does. Do you have an excessive chlorine demand? If you are putting more chorine in the pool than usual, something is using it up and you need to shock.