White particles in your pool might be because of high Calcium levels in your water and it won't dissolve anymore. Confirm your Calcium Hardness level and make sure it is between 250 to 350ppm for plaster pool to avoid further Calcium saturation and scaling. You need to be very careful with your Calcium levels in your water because the only way to lower Calcium in your water is to partially drain and refill your pool water till you get the recommended levels.
Which chlorine are using to shock your swimming pool? Calcium Hypochlorite (granular) chlorine comes with high Calcium levels and in long the run will raise your Calcium levels without knowing it. We recommend using Sodium Hypichlorite (liquid chlorine) to shock your pool, otherwise, you will have to balance your calcium hardness level every time you shock your pool using Cal hypo.
Apart from scales and white particles, high Calcium levels will also make your pool appear cloudy. Low calcium level will also corrode plaster from your pool and the white particles could be plaster or cement, as such, always make sure your Calcium level is within the recommended range.