I switched to natural cold processed bar soaps years ago. There’s a lot of choices on the market, just not in the big chain stores. Etsy is a good source but the search is lacking. It’s time consuming to search. Every place like that has bad shops. I don’t buy from a shop that doesn’t have information listed about the shop. (Where they source the ingredients, do they grow their own herbs, goat milk, etc) I hear it’s easy to make soap. It’s not something I want to do. Bar soaps like this have a wide range of ingredients. Mango, coconut, shea, avocado, cocoa butter and more are available. Essential oils are used in most soaps like this. The different butters & essential oils each help improve skin conditions. I stay away from fragrances, it’s a personal preference. Many people use natural safe fragrance. I prefer essential oils to a fragrance oil. I’ve been ordered from this small company about a year. It’s more than I like to pay, however I trust the company has quality products. If you search on Etsy double check ingredients. I’m seeing a lot of soaps with out lye or Sodium Hydroxide. If it doesn’t have one of those ingredients it’s not soap! It’s most likely a lotion bar, which are great for skin. I don’t like lotion so I use lotion bars, oil or body butter.

https://www.ettaandbillie.com/

This is a good company:

https://www.chagrinvalleysoapandsalve.com/

Another option is Castile liquid soap. There’s many good options on the market. I just like bar soaps so I don’t know a lot about it. Many people make their own liquid soap using Castile.

Tallow is good in treating eczema. (Beef fat) Many bar soaps has tallow as an ingredient. Tallow body butter is great for the skin. Most of these have other butters and maybe essential oils.

Essential oils are great but like anything else it can be unsafe if not used correctly.

Also, most skin conditions are a result of food sensitivity or allergies. I’m not an expert, I read a lot about natural medicine & I keep seeing this.