No, the Japanese military did not drop any bombs on the USA after the atomic bombs were used on Japan. The bombs and pending invasion by the Soviets and the Americans (and allies) motivated the Emperor Hirohito to surrender to the Allied Forces.
The United States Used Nuclear Bombs Against Japan After The Pearl Harbor Bombing, And So The United States Dropped A Nuclear Bombs On Hiroshima. Japan Said That Didn't Matter, And The United States Dropped A Nuke On Nagasaki.
If you are referring to WW2, then the US stopped using atomic bombs on Japan because Japan agreed to surrender. Had they not, the US had plans and production setup to drop a total of 23 atomic bombs on Japan in 1945.