@LionelMessi2007 Congrats for passing that rating, puzzles are great and your puzzle rating is very nice, play and analyze your games. I believe you cause i myself have seen 1800 players with 2587 puzzle ratings, you are doing great!! you can be a master easily if you keep working on all aspects of your chess.. And don't play bullet or blitz, rapid and classical are the way to improve if you are serious about it.. and of course anaylyzing, and learning new things. just go for it. you are 13 and your rating is very good.Go for it :)
And to answer your question, puzzle rating is not representative of your real rating... You need to be good at all aspects of chess to be a good player, but tactical ability plays a big part :).