While the USAF does have helicopters, we don't have nearly as many as the Army.  Your best bet would be in the Army. 

USAF helicopter pilots go to UPT and learn on the Texan II first, then track select to go into helicopters (with further training in UH-1s).  I don't know how many helo slots there usually are, but I'm going to guess that there aren't many.  The only helicopters the USAF uses are for special operations and guarding missile bases.