Can my side by side be recharged?
yes it should be able to be re-charged.
It will be expensive as you need a pro. Also there is no use recharging it unless the leak is found and repaired.
Often it makes more sense to put those dollars towards a new unit.

I would confirm that it is a low freon problem.
Symptoms are that the compressor runs all the time except when in a defrost cycle. You can usually hear the compressor but also should be able to feel it vibrating and it should be warm.
Also there will only be frost in one area of the evaporator/freezer coils after it has run continuously for an hour or so, usually where the freon enters the coils.

Note: There are several things that can cause a freezer to run warm.