Here's a short answer. If you want a much longer and more complete answer, Alfred has a Ship Repair 101 thread that's very good, but which might take you quite a bit of time to digest.
Pearl will be overloaded after almost any decent first turn attack by the Japanese. As a rule, most Allied players will move damaged battleships to the West Coast (when they are sea-worthy enough to make the trip, when the Allies are sure the KB is gone, when they've set up at least some ASW support for the trip, etc, etc.) The West Coast has several shipyards large enough to handle battleships (Seattle, LA, San Francisco, Mare Island an Portland can all handle at least 2 BBs each) - just don't overload the yards there, too - spread your damaged ships around. Also, make sure not only to put your ships into port, but to put them into Shipyard Repair mode once they are there - otherwise your damage, if major, will never get fixed. I think this may be your current problem. Anyway, good luck and have fun with the game!