Air Conditioner has sediment or something in it...clogging the drainage line.?

I've been having a problem for a few months where water comes up through the floor tiles. I figured out it had to do with the a/c's exit pipe - but I thought when it rained it blocked the exit and caused the water to back up.

I did a few things to correct the problem and it worked for a few weeks and this morning the problem was back.

So I took the shop vac and attached it to the a/c and a bunch of what looked like mud came out. Not only that but when I was running water through the unit where no mud should ever be...crud kept coming out.

-- some background - a tornado hit my house back in feb and two trees ended up ontop of my house and in my house and I guess I thought the a/c was ok. So, how did crud get into the unit?

I flushed the pipes unit everything ran clear. Do I need to call an a/c repairman? Any help would be appreciated.