I personally have bad eczema and my baby is starting to develop it too. What I find best works for me is fish oil supplements. I know it comes in liquid form for babies too. Just check with your pediatrician when it is ok to start giving. Mine said as long as she is eating solid food I can give it.
I had really bad eczema when I was younger and cortisone can actually have the adverse affect and make it a lot worse, I would reccomend putting oatmeal in a sock and giving your baby a bath, using fragrance free soap only, and putting pure castor oil on their skin, that should clear it up immediately if it is eczema
My baby has this right now under her neck & cheeks. Doctor told me it was drool rash mixed with sweat rash since she is on the chunkier side. Is your baby drooling more than usual? Teething?