What you have is chips that have broken through the clear but not the colour layer most likely, so to make them "go away" using polishing you would firstly be at it for days and more importantly you will be removing the clear from the areas around it to make them disappear and you DON'T want to do that.
A filler polish won't do the job either, at best, they cover up the odd bit of scratching in the clear by smoothing it out so to speak, they won't fill the marks you have.
Don't worry, it is a common misconception about how much you can fix with even the best rotary and polish etc, they fix minor scratches on the surface of the clear top layer that look bad because they have sharp edges. Polishing basically removes those edges on the deep scratches meaning that they don't reflect the light so much. Minor stuff (holograms, swirls, marring) goes away with hard hard work.
If you look at how your car is painted you basically have (from surface down)
Clear coat, then colour, then primer, then the metal/plastic body panel.
Great example here of the make up:
http://www.theultimatefinish.co.uk/car-care-blog/wp-content/uploads/2011/09/Paint-Defects.jpgYou are basically looking at paint to bring it UP to the level of the surrounding area because you have no clear left to work with in those marks you have. You can imagine if you polish down to them to level them out you are going to have the paint around it also down to the colour coat - not good!
Now the good thing is that providing the colour is intact now you have removed the polish residue, you can possibly get away with dabbing some clear on it using a paint spear. Create a dome that is higher than the current clear by layering it . Then you can use wet and dries (very fine grades still though) followed by refining with compound and polishing to bring it back down to the area around it thus correcting the issue
A kit like this (used them myself to do exactly like I am describing but on full on down to the bodywork chips) will do the job:
https://www.paints4u.com/ProductDetails.aspx?productID=6912Just be mindful that you are looking for the best result, not a perfect factory fresh finish - which can only realistically be achieved by respraying I am sad to say.
Just remembered there was a guide on Detailing World on this very subject which I followed first time I did it:
http://www.detailingworld.co.uk/forum/showthread.php?t=20127
