Don't be tempted by shampoos for greasy hair, especially when you are washing it frequently - they contain some pretty harsh detergents and actually encourage the production of sebum (the 'grease').
I have always had greasy hair, but as I also have scalp psoriasis I simply can't wash it every day (if I do, the psoriatic patches get really sore and crack). I use hydrating shampoos that are gentle on my scalp, but seem light on my hair (the Garnier one with oat milk is my current favourite), and find I can go longer between washes as my scalp isn't irritated and therefore stimulated to produce more sebum.