Crappy water, old pipes, I rent. What is the most inexpensive way to get your hair washed. ?

How can one get there hair clean w/o washing it over the sink every morning with distilled water? My super watershowerhead filter is not doing anything. The water leaves a grease slick on my hair and it is falling out as I can't even brush it. My landlord refuses to believe the water is any different then anyone else's. I think the hot water heater needs flushed, it has been vacant here for 3 months and crap comes out of the tub spout when only the hot water is running at first too.