particles in well water that were not there before indicate something has gone differant down in your well. Filtering at the tap is just a stop gap measure.
Your going to have to have the well intake checked. If you have a sand point the flexible line inside the liner can be pulled up and checked. If you have a strainer type intake the reason is usually caused by it being installed or falling too far down and near the bottom where it is picking up sediments.

Depending on your well the worse thing that can happen is a detereration of the sides of the well and it caveing in. The bottom would now be up near the intake and hence picking up sediments.

Whatever the reason, it's down in the well and installing a tap filter will not solve the problem. it will just lead to more maintenance cleaning a filter that will never end.

Your well guy was givng you the right fix for a temporary silting caused by heavy rains or an earthquake tremor. But if you still have silt after a week you have a serious problem that will need you to pull the well intake pipe.

Not a costly fix compared to drilling a new well but expect a hefty bill from the well diggers. And don't wait too long. Silt is abrasive and will ruin your pump & fittings, and ruin any washers, dishwashers or other appliances.