Disc brakes make noise
In short, squeaking brakes are caused by the sound of your pads sticking then slipping increadibly quickly, rather than applying presssure to your discs smoothly.

Solution:  Sometimes these problems can be a right pain in the butt.  Sometimes your brakes need time to bed in, sometimes, as you know, your discs just need cleaning, or importantly, drying. But if that doesn't work you need to rough up your discs.  You can get products with abrasives in them just for this purpose, or, less expensively.. I know many people have had success with very fine sand paper.   

Give that a try before replacing your discs.