can my job fire with a statement they made me write under false pretenses?

[Liz]

i was fired from my job on my birthday none the less for force balancing my drawer( i was a teller ) . what happen was that during a routine audit of my drawer , my assistant head teller discoverd my drawer was short 10 dollars. i had told her that the difference was from sunday and that since i called off mon that i couldnt run the difference. well anyways they took me into the conference room and told me to write a statement saying that i knew the difference was in my drawer and to sign it. they told me to write it only to attach it to the audit and get the mistake corrected , however they then asked me into the conference room again to tell me that i was terminated because i admited to knowing i had the difference and that i violated a policy. the only proof they had was the statement i had written. only to discover later that they lied in order to get my statement and fire me. i filed for unemployment and it was denied because of wilful misconduct. do i have a chance at wining the appeal if i get a lawyer and the fact that i never had any such thing on my record before this?