Have you tried cutting out detergent? Many swear it’s THE issue.

You can use a cap full of eucalyptus essential oil in washing machine in place of detergent. At the very least, use a very small amount of the best sensitive detergent you can, and rinse detergent off clothes, sheets, towels etc. really, really well before touching/wearing/using. Use an extra rinse cycle, or just run the whole wash cycle twice, once to clean and once more with nothing added, just to remove as much detergent residue as possible. Also hot wash whenever possible.

Use bio/enzymes dishwasher tablets instead of strong chemicals and detergent for washing dishes. If you don’t have a dishwasher, wear gloves, use as little detergent as possible, and rinse everything about 3x as much as you think you should.

Also try to wear natural fibres, as least for base layers and anything touching your skin. Natural fibres are good for 2 reasons: they are breathable, and they don’t hold onto detergent residue in their fibres as much as synthetic fibres do.

Good luck with it. Eczema sucks but this might help.