Freezing the botox will most likely not effect the pain associated with the injections. Botox should be stored in a refrigerator and does not need to be frozen.
I am unsure if you have an eye-BROW droop or an eye-LID droop -- it is difficult to improve an eye-LID droop by injecting the crow's feet. That location can typically only improve an eye-BROW droop...Good news is that this is temporary and will improve with time... The droopy eye-LID...