I run distilled water through my system if the nozzles are not producing as fine a mist as I would like. Your clog may be a bit late for that. Try soaking it in vinegar. You might also take it apart before you soak it in vinegar.
I soak my shower heads in CLR and they work like new I would think they would work for the nozzles too. I use distilled water and never had this issue with mine.
so it turned out my nozzle heads have a core that can be screwed out ...
I think it got screwed to tight by the water pressure so now I loosened it again and it should work again.