I am a bit in the dark myself, and while the thought of applying again makes me cringe I think I may need to. I read an article saying that one of the best things to do if you get rejected is to contact the schools (after the application madness dies down) and ask how you could strengthen your application.
As for whether or not you should apply to the schools that rejected you, if they are still a good fit for your research interests I absolutely would.
On the bright (?) side, every rejection makes me a little more numb for the next, and there is the added bonus of concocting some excellent cocktails.
Good luck!