If you post your model number, I can give you some better ideas of what the problem is. I've fixed several refrigerators, over the years, and they can be a pain to work on. I can fix most problems, except when the compressor fails...that can be more expensive than buying a new refrigerator. You can go to a web site called "appliancepartspro's.com", enter your model number, and get some idea of what parts can cost. Unless you are fairly handy at fixing things, and have the tools, you will almost have to call a repairman.
About the Only thing you can do is to check that the condenser coils aren't clogged with dirt and dust. Most newer refrigerators have the coils mounted near the floor, instead of on the back of the fridge. These coils are subjected to all the floor dirt that builds up over time. You should see a grill under the front door, and you can pull this grill, then take a flashlight and look to see if they are dirty. If so, and you have a vacuum with a small wand, and a parts brush, you can clean most of the dirt of the coils...this is an awkward task for a lot of older people, but is probably the most common cause for troubles. I clean ours twice a year.
Beyond that, the "cold control", or the "defrost timer" may be going bad. If you are getting ice buildup in the freezer...you mentioned icicles...the defrost timer would be suspect. It is supposed to turn on a heating coil in the freezer compartment for a few minutes, every day, and defrost the freezer, draining the water thru a tube into a tray in the bottom of the fridge, where the fan evaporates the water. If this isn't working, the freezer coils will clog up, and the entire fridge will stay running trying to complete this cycle. It's usually a 50/50 chance that either of these controls can be causing the problem, and its a good idea to replace both at the same time. The parts costs will be in the $150 range...and if a repairman is called, you can expect to pay double that, or more, with labor, and their markup for parts.
Bottom line...if dirt on the condenser coils isn't your problem, start watching for a sale on a new fridge...as calling a repairman will probably cost you 2/3rd's the price of a new fridge.
