Ice Maker leak

I have an Amana side by side with an ice maker that is leaking. It works fine, but seems to make hollow ice cubes and there is a drip that forms an icicle near where the water goes into the maker. It then freezes and gets stuck before it can dispense very many ice cubes. I use the hair dryer to melt the ice, it works for a little while then freezes again and stops working. We suspect the water valve is leaking, but could there be another problem?