(As a life long eczema sufferer) It’s entirely possible the material is irritating your skin but eczema is an immune response so (if you’ve never had it before) it’s more likely to be dermatitis (inflammation of the dermis). Try wearing a different top for a few weeks and see if it gets better?
I find everything I wear riding has to be as breathable as possible otherwise I get sore patches where I get sweaty and hottest; my neck, back and shoulders.
Keep strong soaps, shampoo and and shower gel away from your sore bits and use aqueous cream or white soft paraffin (from chemist) to moisturise and as a barrier before riding.