[size="200"]CRAAAAP, I HAVE AN EMERGENCY![/size]
So the toilet got stopped up, and now there is BROWN, FILTHY WATER FLOODING MY BATHROOM!
My parents are gone now, finds out about this he will be
pissed out of his mind!

Obviously I can't soak up the water with bath towels, because that would ruin the towels, so I've been using paper towels to clean this up. I've been picking up the... gross bits.... and running over and flushing it in my parents' toilet. Is there anything else I could do?
You could use a wet/dry shop vac if your parents have one. Vacuum up all the poop water and dump it somewhere.