Welcome! Some people need to wash frequently whilst their scalp adjusts, and they get used to good technique, sometimes daily. Use loads of co-wash and build up a light lather.

Secondly which product are you only rinsing part way, your co-wash? You need to rinse that thoroughly with massage just as you would rinse out all your shampoo, some co-wash products will literally give you squeaky clean hair.

You don't mention a rinse out nor a leave in conditioner, it's the rinse out you are not supposed to wash out fully, tho some of us do prefer to do so.

It's as likely the Shea Moisture that is building up as your conditioner, that contains shea butter and coconut oil which can certainly give sticky and greasy build up if overused or on the wrong hair type. Did you choose your products based on your hair properties and dew points?
2a-2c, medium texture, porous/ colour treated. Three years CG. Past bra strap length heading for waist.

CO-wash: Inecto coconut/ Elvive Volume Collagen
Treatments: Komaza Care Matani, coconut/ sweet almond/ fractionated coconut oils, Hairveda Sitrinillah
Leave in: Fructis Sleek & Shine (old), Gliss Ultimate Volume, various Elvive
Styler: Umberto Giannini jelly, Au Naturale styling gelee
Flour sack towel, pixie diffuse or air dry.
Experimenting with: benign neglect