thanks for your patience.
It seems to be seborrheic dermatitis.
Since its an eczema, its recurrent. But we can always try to keep it under check.
I would recommend the following:-
the best treatment to treat it is to apply steroid lotion and anti fungal cream over it.
lotrimin cream mixed with cortisone lotion, twice a day for 2- 3 weeks.
washing with nizoral shampoo thrice a week is recommended.
After 2 weeks,, elidel cream can be considered for application. But it will require a prescription.
you can take oral antihistaminic tablet claritin 5 mg once daily in the morning for a week, to control itching, if any. Also it will help to control the allergic process and will be helpful.
Also application of coconut oil on the scalp will be beneficial.
Hair thinning is reversible. It will improve with treatment.
these are my recommendations, hope they are useful.
please feel free to ask me in case you have any queries.
hope this answer was useful.