It sounds like you've got some contamination on the paintwork, but just to check, they are not stone chips are they?
If it is contamination, then you need to decontaminate. An easy way to do this is by getting some decontamination products. Two excellent and highly regarded products are Autosmart Tardis, for tar removal and Carpro Iron x for iron / industrial fallout.
After washing the car, you spray on Tardis, let it dwell for about 3 or 4 minutes, you will see the tar start to run, then agitate it with a cloth, then rinse thoroughly. Then spray on Iron X, beware the smell!, leave it for 4 or 5 minutes. You will see as it reacts to the iron contaminants that it turns red/purple. Again you can agitate with a cloth to help the process but no need to rub hard. Then rinse thoroughly. Don't let either product dry on the car. Do a panel at a time. I throw away the cloths After using these two products as they are very pungent.
After using these 2 products your paintwork should feel a lot smoother. A lot of people these days don't bother claying after doing these two processes, as they are excellent at what they are designed for. If you have a wax on your car, you will need to reapply it where you have done this process. If you have a synthetic sealant it will have reduced its effectiveness, so may be worthwhile reapplying.
So doing it this way, you don't have to worry about claying and you get silky smooth paint back again.
I hope this helps you out.