Do you trim the ends very much? The dry frizzy stuff is just dead ends of the hair from coloring so much. It is also the split ends and they will look frizzed when they dry.
I know my hair will get like that too, but my hair is naturally oily. I do condition it everyday though because if I didn't I wouldn't be able to brush through it. The conditioner I use is Suave conditioning. It works well even when I've colored my hair. Also, when you condition (this is hard to do), but don't rub the conditioner into your scalp. Just rub it on the ends of the strands. Like an inch or two from your scalp all the way to the ends.
Make sure when you comb it, you start at the bottom and don't tug!! Because of coloring it will break easier.
I'm not an expert, but these things have all worked for me. Good luck!!
I had to come in to edit.

I thought of more. I also do NOT comb or brush mine after it has started drying. This will always frizz out the ends. Something else, if you like mousse or gel, put that on the ends and it will keep away the frizz look, but if you don't like the wet look of it, you'll have to blow dry it for awhile. Just don't comb or brush it when you're done.
I don't know how long your hair is, so some of this may not even work for you. My hair has been almost to my butt for years, so things like the mousse/gel work for me.