Sounds lke the defrost drain is blocked.
There are three common places where blockage occurs.At the drain, in the freezer. Iced over due to an obstruction. In the transition between the freezer/fridge/drain iced over from an obstruction. Ath the bottom back of the fridge where the defrost drain hose meets the defrost pan hose. The def/pan hose is undulated lke apiece of under sink plumbing (for most the same reasons). This is where the obstruction is most like to iccur.
Seperate the hoses and run a coat hanger or other appropriate flexible wire throught he pan hose and look for icky junk coming out (blowing through it is optional depending on your personal sanitary necessity level). Yo will know if this is the cause bout immeadiately.
The other places are a bit more difficult to observe and mat take more disassembly.
The drain begins under the evaporator, in the freezer, so you've usually got take the floor and back panel out of the freezer to see the drain. OTOH when I worked for Sears this drain cleaning would cost around $100. Depends on what your comfort level is as far as disemboweling you frifdge goes. Remember neve use anything sharp to defrost your freezer, hot water or a hair dryer are better choices.