Hi Roman,
Does your Timer0IntHandler(), clears the Timer Interupt?
You need to clear the Timer Interrupt. See below from the timer example program. I admire your coding with direct address read/write. However, I would recommend using the Tivaware API's. Much more readable.
void
Timer1IntHandler(void)
{
//
// Clear the timer interrupt.
//
ROM_TimerIntClear(TIMER1_BASE, TIMER_TIMA_TIMEOUT);
}