dont't worry about the bald patch. It will eventually grow hair. My son also had a bald patch and now it's filled with hair but it took some time. It wasn't till after he was 1 year old that he has hair on the front part of his forehead.
As for the dry flaky scalp, it's most likely cradle cap which could result from triggers such as dryness, food allergies from breastmilk etc. Eczema simply means allergic rash, which means there are triggers to it.
Continue to use the things that the doctor gave you. The dry itchy scalp should go away in 1-2 weeks time.