Your drain tube may be stopped up with ice at the upper end because it drains too slow because it's stopped up at the lower end in the evaporator pan under the unit at the floor. It can get dust and mold in it. Once you get the ice out at the top a little air pressure will usually clear it out. Flushing it out with hot water and clorox may help. Make sure it drains quick enough. The drain should be located below the evaporator coils on the lower back of the freezer.

I have the same problem on a Kenmore 10679202990 but it is reaccuring. About every 2-3 months the drain tube freezes. I use "clean" rock salt to melt the ice and hot water after it has melted through. Then I use air compressor to blow the tube dry and to make sure it is clean inside. I have read Amana has a kit to fix the same problem with some of their frige, does kenmore have same thing?