It can take weeks or months for dietary deficiencies or imbalances to translate into improved health or skin depending how nutrient dense and varied your new diet is. You may well find you get improvements later down the line since the turnover of the epidermis is anything up to two months. It also takes time for the gut lining to heal, intestinal flora to rebalance and any issues with nutrient absorption to normalise. Obviously your immune system is fighting you at present, that could well slow down the time it takes to get a positive result unfortunately.
Bear in mind too that you may have worsened the issue by further damaging your skin barrier with some of your home remedies so set yourself back. Are you eating plenty of healthy fats especially omega-3s from oily fish, omega-enriched eggs and seeds like flax and chia now?
Without knowing the cause we cannot recommend an effective topical treatment, what is good for one scalp complaint can worsen another. A skin rash would suggest inflammation which makes sense in lupus, that is NOT the same as xerosis as you self diagnosed. The best I can suggest is be kind to your skin barrier, only use products at pH 4.5 to 5.5, gentle anti inflammatory type ingredients like aloe vera inner leaf gel. Otherwise e-mail or telephone your rheumatologist or make an appointment with your family doctor.
2a-2c, medium texture, porous/ colour treated. Three years CG, growing out mechanical and chemical damage = breakage and very high porosity. Past armpit length heading for waist.
Treatments: Komaza protein, Komaza Matani, coconut oil with sugar syrup. Hairveda Sitrinillah
Leave in: Fructis Sleek & Shine (old), Gliss ultimate volume
Styler: Umberto Giannini jelly, Boots curl creme, Rockin RInglets
Experimenting with: Mega-Tek, Curl Harmony reviver, Elvive Full Restore 5.