I am in week 5 and my hair is...well, I wouldn't call it greasy; there is something more akin to a waxy coating on it.
Lisa, do you live in an area with hard water? We have water here with hardness off the scale, and I can't use it straight out of the tap to wash my hair because I get the same waxy coating. (I can't drink it, either, because the level of calcium carbonate rips up my stomach.) What I have to do now is boil a pot of water for about 5 minutes at a rolling boil, which drives off the excess carbonate ions and softens the water. Then I mix it with baking soda and use that, followed by an apple cider vinegar rinse, to wash my hair. Works perfectly and no more waxy buildup. I also usually run the boiled water through a Brita pitcher, but that's more for my stomach than anything else.