baby CRADLE cap SOS

My baby is having cradle cap spreading all over face n head. Any parents out there having same issue? How did you solve it? I have been oiling with olive oil on baby hair and skin for 15-30 min before bath. I wipe away the olive oil without rinsing with any shampoo. I gently rub my baby scalp and face/ear to remove cradle cap but it keeps appearing and spreading to more places such as side of scalp. Any more solutions to improve situations?? I have tried this for almost 3 weeks and cradle cap still alot. Am planning to purchase cradle cap comb + mustela foam shampoo to try. TIA ----Edit----- I bought the cradle cap comb + mustela foam cleansing. 1) before bath, oil baby hair with olive oil for 5 min 2) using comb dip in water, scrub baby scalp till forehead gently in circular motion for around 5 min 3) foam up shampoo onto baby hair and scrub with comb for 5-10 min on baby scalp till forehead 4) rinse off with clothe for a few times until shampoo is gone 5) wipe baby scalp with clothe to remove debris of dead skin I have been doing for w 2 days and baby cradle cap has improved alot. I'm wondering how to clean her ears and eyebrow. Will be trying soft toothbrush