I have a GE side by side refrigerator with Ice and Water in the freezer door. The water line in the door appears to have frozen up. I don't get water, but I do get ice and it is making ice.

The problem is with the formation of an ice block in the water line inside the freezer door. My solution is as follows:
1. Before you start you need to remove the ice already formed.
2. Get a small syringe and fill with hot water
3. Push the hot water down the water line dispenser.
4. This should melt the ice block and water should start flowing again
5. Once the water starts dispensing, you can proceed to fix it.

6. Get 3 ft of hedge trimmer line. This is a hard flexible plastic line.
7. Insert the line into the water dispenser.
8. Push in about 2ft 6 inches of the line into the dispenser.
9. This should leave a 6 inch tail outside. This is your tug line (life savior)
10. Now the next time the ice block forms inside the water line, it will form around your hedge trimmer line also.
11. The next time the water line freezes, tug on this tail and your ice block will come out
12. Insert line again like Step 6 after water starts flowing again.

Another option to the syringe solution above is to use some thin plastic tubing (as suggested by rockhopr) like 3/16" OD Power Care Fuel Line in the lawn mower section of Home Depot ($3). Then I drilled a 3/16" hole in the cap of a water bottle and fed the line through. Then filled the bottle half way with hot water and fed the line up the water nozzle. You'll want to have a bowl or short glass in there to catch the water and be sure to hold down the water dispenser trigger. Next, turn the bottle upside down and gently squirt in the hot water working the plastic line as you go. Took less than 5 minutes.
And I followed the hedge trimmer line "plug eliminator" as suggested

How do you get to the line to put the hot water in it?