Whenever I have appliance problems, I go to http://www.repairclinic.com/ . Click on "repair help." You can usually figure out what's wrong and then buy the part or have a service tech fix it. Here's what the site has for your particular problem:
"The food in the refrigerator freezes
This is a common problem that often doesn't have a clear, permanent solution. The first thing to check is the overall internal refrigerator temperature (see the Appliance Accessories section for a refrigerator/freezer thermometer). The proper temperature should be between 35 and 42 degrees. Here are some things to try:
If your refrigerator temperature is closer to 35 degrees, try turning the temperature up slightly.
If you find that the temperature varies a lot from the top shelf to the bottom (where it is coldest), try putting produce and other sensitive products on a higher shelf.
If the temperature is too low and you can't make it warmer by adjusting the thermostat, you probably have a defective thermostat. If so, you need to replace it, because they cannot be repaired. Other possible problems are a leak in the sealed (refrigerant) system, cold air migration (in side-by-side models) or a defective air damper. These problems can be quite difficult to locate and correct, we recommend you contact a qualified appliance repair technician."
Good luck!