Tarena, it's been my experience with Amana that tells me you have a failed water inlet valve.
Here's how it works; Water comes from the wall into the fridge to the valve I'm talking about. Now this valve works like this... When you put a cup in the dispenser area to get cold water a switch sends 120 volts to the valve and it opens up allowing water to flow through it. When you remove the cup, power is shut off at the valve... the valve is supposed to close all the way, if it didn't there would be water dripping from the dispenser area, right? (Like a leaky faucet) If the valve is bad, it won't open at all. (Like a blown out light bulb)
The ice maker is similar. When it "harvests" ice and it drops into the ice bin, the IM will send 120 volts to the valve (for 5 seconds or so) to re-fill the ice mold so it can make another batch. Now when the power is removed from the valve, it's supposed to shut off all the way. If it didn't, there would be water dripping into the ice maker fill tube (in the freezer behind the ice maker). drip, drip drip... one after the other.
Let's assume that the ice maker valve didn't close all the way. What would happen then? As these drops of water enter the freezer compartment and are heading down the ice maker fill tube toward the ice maker, they don't make it all the way 'cause they FREEZE in the tube! One drop at a time, week after week. ('course you never notice it, 'cause it's in the freezer) Now... the ice maker is still trying to make ice, so every 45 minutes or so it sends 120 volts to the valve to get more water. But the water fill tube has ice in it because of the water drops that have accumulated there. This goes on over time and eventually the water fill tube becomes completely BLOCKED with ice due to those water drops.
Now what happens? The ice maker is still trying to make ice, but the fill tube is blocked... it can't get water through it. But when the water valve opens up to allow water to the ice maker, where does it go? Since the fill tube is blocked, all that water pressure builds up in the water line (tube) that feeds the ice maker and eventually it blows out! (you can verify this... pull the refrigerator out from the wall, look at the water line going to the ice maker. There's a connector back there for the tube to fit into. This is what's blown out.) Now the tube is just dangling there and not hooked up to the ice maker any longer. Since the ice maker is still running, every time it asks for water it sprays out and onto the wall and floor back there through this dangling tube.
The repair? Replace the valve. It's easy. The part number is 67005154 and it lists for about $21.00. You can find one at any appliance parts retailer. (you'll see where the valve is located... it's where the water line hooks up behind the fridge.) UNPLUG YOUR FRIDGE WHILE YOU WORK ON IT!!!
Just replacing the valve is only half the job. You'll still need to remove the ice build up in the ice maker fill tube. Do this by pulling it straight out the back of the refrigerator and putting it under warm running water. Then re-install it and hook the water tube back up to it.
On some models, you can not remove the fill tube. If you can't get it out the back, you'll have to do it from the freezer compartment behind the ice maker (a little more work, but still do-able). It's easiest by removing the ice maker.... pull the ice bin out and set it aside. Then remove the 3 screws holding the ice maker. You don't have to disconnect the wires, just try to get it out of your way the best you can. Now take a hair dryer and thaw out the fill tube until the ice slides out of there. Then rebuild it.
There ya go! Job time? about an hour. Part cost? about $21.00. Knowing that you fixed it yourself? Priceless.