H4 means you're a dependent of an H1B visa holder correct? One of your parents? You have the wrong visa for temporary work and probably should have switched to a F1 prior to starting flight training.
You need an experienced immigration attorney. Spend some money and go see 3-4 attorneys and pay for their advice.
http://www.immihelp.com/forum/showthread.php/114432-change-of-H4-to-F1-visa