I would like to know how many battleships and carriers the US Pacific fleet had throughout the war.
Counting only fleet carriers.
At the start of 42 the USN had 10 battleships and 8 carriers.
During 42 4 new battleships and 3 repairs from Pearl Harbor joined the fleet; 5 carriers were lost and one joined the fleet.
During 43 2 new battleships and 6 new carriers joined the fleet.
During 44 2 new battleships and 2 repairs from Pearl Harbour joined the fleet; 7 new carriers joined the fleet.
Before VJ day in 45 3 new carriers joined the fleet.
This ignores time spent in overhaul and repair aside from those damaged on Dec 7th 41.
I have included two official websites here for you to learn about the US Navy in World War 2.
The first link will show every ship in operation starting 1940 and commissioned during the war. The list breaks down each ship by class and notes how they were lost during the war. This list also provides a breakdown of the ship size, armament, crew compliment, and total number of aircraft carried. This will provide you every aircraft carrier and battleship.
HyperWar: US Navy Ships, 1940-1945 (ibiblio.org)
The second link is to the Naval Heritage site. This will provide with a total strength of the US Navy year by year. The site also provide a listing of all US Navy and Coast Guard ships lost in the war. It also provides many photographs and histories of the ships that served during the war.