Hi! It can be so exhausting going through dry scalp and face eczema. I've had seborrheic dermatitis for 15 years now on and off. Just got a grip without it coming back 3-years ago and recently wrote a detailed article of the journey that may be published here soon.
Dandruff is often just the same as seborrheic dermatitis, it just gets at its worst when it has to be diagnosed and treated properly. If you have a history of atopic dermatitis or eczema then it is very likely SeboDerm. A dermatologist would be best to get officially diagnosed and treated. If you trust you GP then for quicker relief possibly contact them if they suggest a prescribed shampoo until getting to Derm.
Giving a steroid CREAM for your face and scalp especially SeboDerm is very concerning. What I've always seen given and others that I know who have it is red gel based shampoo that does have steroids in it and it has always gave much relief and a cleared scalp within 2 weeks. The maintenance along with using that shampoo is what's also important. The dermatologist may suggest a good dandruff OTC shampoo to maintain or if you're like me and likes natural products, then looking for shampoos with Peppermint, Neem, or Tea Tree if not allergic, has done wonders for my scalp.
Lastly, SeboDerm is nothing like atopic dermatitis, as it's ultimately a fungus and one dermatologist I had an appointment, who had SeboDerm himself told me that it will only be killed by combating the fungus with the right ingredients in a product. The shampoo often given has Zinc and other ingredients you may see along with the low steroid dosage which calms it quicker. I also would get the SeboDerm travel to certain areas of my face at its worst. SeboDerm is very very similar to Psoriasis so if you want to know which you have go for the biopsy if able, but ultimately the healing is just as similar. Atopic Dermatitis healing methods which is often over moisturizing will not work for SeboDerm. You scalp is already too clogged. Hope that long explanation is helpful. Please get guidance from a dermatologist, when it is a new problem it can be very overwhelming!