The black stuff could be charcoal from the filter. Maybe try to rinse the filter before putting it in. If the first faucet you turned on after you put stuff in the line was the kitchen then there is stuff in the screen. Take the screens out and put them in a disposable cup of CLR. Follow their directions.
Good luck.

Through the years when someone with well water mentions black particles that clog the aerator or appear in a filter, I have found the culprit to be deteriorating galvanized pipe. Check all along your water line and see if there are any galvanized fittings such as elbows, reducers, etc. Even check the nipple the pressure switch is mounted on. The pieces are the inside of the pipe deteriorating.

I don't think there is charcoal in the filters that I use, but I will check. I don't have galvanized pipe in my water line system, it's all copper. Once in awhile I get black particles in the faucet screens, but not enough to slow the water down. One time when I had the well worked on the repairman told me to pour clorox down the well to disinfect the water. I wonder if that would clear up the particles. Also,the toilet tank water is black. What causes that??? Thank you for helping me, thank you thank you.

I'm not saying this is your problem but to help you without being there, we have to do it by process of elimination. If this isn't your problem, you may be looking at a more serious problem. You very well may have copper lines throughout. But to be sure to eliminate this possibility, still check at the hook ups at the pressure tank and also at the nipples coming out from the wall to feed the faucets' lines and also the toilet valves.

Hi, I have two small galvanized pieces attached to the well line coming out of the wall. On the toilet there is a chrome elbow shutoff going to the toilet.

Could also be the pump going bad. The impellar could be wearing out. What type of pump do you have?

The pump is attached to the bottom of the well water pipe. (submersible). Not sure what brand it is.

Take a look at the particles through a strong magnifying glass, jewelers loop or even better a cheap microscope. If the particles have a layered look or look to be a layer from something, then it is from the inside of your galvanized fittings. They'll be black, some a bit oblong and may taper on either or both ends. They are pesky, even just one small fitting can give you these particles as it deteriorates. The outside of the piece can look brand new, the inside is coming apart. You'll know over time since under pressure, the fitting will eventually and suddenly blow open once it weakens. Another tell tale sign is when you seem to be losing volume at a spigot or even coming in from the well to fill the pressure tank.