Yeah... I have something similar to eczema (serrobhreic dermatitis, I just have Google autocorrect it for me when I need to put it on a medical form.) All the beauty blogs and subreddits say "stay away from salicylic acid" so I tried all the alternatives in the literature, up to and including literal tar shampoo. Brackish, sticky, thick, smelly tar. Nothing in the medical literature works anywhere near as good as salicylic acid, and I have one brand (shampoo) that works for my face and scalp that's more moisturizing, and another (bar soap) that works for my body. If I skip showering for 1-2 days, my red scaly oily skin starts to return and I get face acne and bacne.. It's not fun. But as long as I keep my regimen (which also includes a specific lotion and a specific cleanser) and get enough sun (tanning in winter months) you wouldn't even know I had a skin condition.

It took me many years (including over a month using NO products as many suggested the products were the issues) to find this regimen. So I'm sticking to it.