Need assistance on H1B

Can someone assist me? I currently hold an H1B visa with TCS. Despite repeatedly following up with management regarding my travel they have not approved it yet, stating that many deliverables need to be handled offshore. They are not even allowing me to move to a different project. I feel stuck with no progress and have already lost an entire year.

Is it possible for me to move out of TCS and find another employer who can take care of the H1B amendment? Does TCS allow me to file a transfer to another company if I choose to leave them?