It sounds like swirl makes from poor washing techniques.
Swirl marks won't be fixed by washing or claying. In fact claying can be a cause of swirl marks or scratches if not done correctly.
Polishing, waxing and sealants can possibly provide some very minor correct or filling in of the swirl marks but aren't a permanent fix and it's unlikely it will even fix it up satisfactorily.
In order to permanently remove swirl marks a cutting compound of some kind must be used. Whether a heavy, medium or light cut or a combination of them are required comes down to the severity of the swirls.
Check out the detailing section of this forum. There are some good threads in there especially by Detailer's Domain which have before/after pictures and include the methods and products used to remove anything from light to heavy swirls.