Usually there's a transition period where your scalp tries to get used to not using shampoo. I'm not sure how long it lasts though, from a couple days to weeks. It's different for everybody. But if you stick with it, it would pass.
Anyways, what kind of no shampoo method are you using? Co-washing (conditioner only), baking soda/acv rinses, egg washes, sulfate free shampoo, clay, or those shampoo bar or dr. Bronners whose name I don't remember..? I do co-washing and the occasional bs/acv rinses.
For the greasies, you could try washing more often, if possible. Or some people drizzle cornstarch (light hair) or cocoa powder/cinnamon (dark hair) to soak up some of the oils.