Is slightly high voltage bad for a refrigerator?
I agree with the others that you probably need a replacement under warranty.

Answering your question:

Most motors are rated for the UL label nominal +/- 10%.  The tolerance delivered by many utilities is their nominal line voltage +/- 5%.  The UL label on your compressor hopefully states it is rated at 115v, giving it an actual operating range of 104-126v, notwithstanding the 110v documentation that came with the unit.

Higher voltage than nominal+10% can saturate the magnetic cores of a motor, causing rapid overcurrent and overheating, which exponentially gets worse as the supply voltage is increased.  Generally though, fractional horsepower motors like the one in your freezer are somewhat more forgiving.  Also, these motors are thermally protected with an automatic reset.  Even if the voltage is a bit high and the motor gets a bit hot, the unit should cycle occasionally on the thermal overload, temporarily shutting off and then returning to service.  A thermal trip and reset like this should not cause the freezer to thaw out.