Hello and welcome to healthcaremagic
You seem to suffer from dandruff/seborrheic
dermatitis of the scalp and facial skin.
Dandruff or seborrheic dermatitis is an important cause of scalp itching and increased hair shedding. Dandruff is bound to recur again, therefore people with dandruff should use an antidandruff shampoo to keep the dandruff under check, rather than using a regular shampoo.
If I was your treating doctor I would have asked you to use an antidandruff lotion/shampoo. My choice is 2%
ketoconazole shampoo, thrice weekly for 2-4 weeks followed by once or twice weekly for maintenance. It is available OTC as Nizral 2% solution.
Sometimes a shampoo alone seems insufficient. In that case you should
consult a dermatologist. Your dermatologist might prescribe you a
topical steroid lotion(clobetasol or mometasone lotion), to be applied twice daily for 2 weeks.
The topical steroid lotion can be stopped once the dandruff is well controlled and thereafter the improvement can be sustained with just an antidandruff lotion/shampoo.
Controlling dandruff would improve your hair fall problem too.
Facial seborrheic dermatitis presents as red scaly itchy patches on the face. You could apply a moderately potent topical steroid e.g
fluticasone propionate for the itchy patches on and around the face.
regards