Mucus like sludge build up in AC drip pan.

I live in Arizona where it is imperative to have a AC unit since the temperatures rise above 100 degrees every day. My AC unit is almost always on 24/7 (Doesn't mean it is always running.)

Recently my AC unit started to leak, it had started about a week ago and then stopped for about 3-4 days and then I noticed it started again today after I got home from work. Trying to find the source of the leak I reached into the drip pan and felt it was filled to almost over the rim and the leak was originating from the seams around the edges of the drip pan. I noticed that there was also a thick brown mucus like substance in the water as well when I pulled my hand out (Which I found to be rather disgusting and washed my hands for 5 minutes afterwords). This thick substance is probably causing a blockage in the drain pipe which it why the pan is filled to the rim. My question is: Is there anything I can do to clean the sludge from the pan and clean out the drain pipe? Or is this a case for the professionals to take care of? Also, could this sludge be hazardous to my health and the air inside my home?

Currently I am located in an apartment complex and the management have been less than helpful.

I have taken some pictures of my AC unit and the sludge in the unit (Since I cannot actually squeeze my head around there to see it).