The drain line should run down the outside back of the fridge.
You may be able to disconnect the tubing from the drain fitting to see if the clog is in the drain fitting or the fitting/evaporator drain pan.
I believe this drain pan connects directly to the drain line but am not 100% sure of this. Some units drain into a funnel like part at the top of the fresh food section and then down to the drip pan under the unit.
If plugged a turkey baster with warm water, an air compressor with low pressure or a wire can often be used to clear it.
Also check that it is not plugged with dust etc. at the drain pan end.
You might as well clean the condenser/compressor fan and the condenser coils while you are down there.
If it looks like stuff is growing in the tube I would flush it with a 10% bleach solution. This should kill the stuff and let you flush it out. You may have to do this several times, let it sit for 15 minutes or so between flushes.
Be careful that the drip tray does not overflow and empty the drip tray after you are done.
Be sure to unplug the unit while doing this.
Sounds like you may have another problem.
Your drain line should not have any well water minerals.
It is there to catch water from the frost build up on the evaporator coils.
This is moisture in the air and therefore has nothing to do with you well water.