First of all, sending you a giant hug xx
Eczema is horrible and even worse to deal with when it's your little one that has it.

I've dealt with it on and off throughout my life, including having it on my eyelids. I was prescribed a non-steroidal cream specifically for that which was like a miracle, I can't remember the name unfortunately as I'm too sleep deprived right now, but you could only use the tube for 3 months once opened as it had no preservatives and the GP had to ring through for permission to prescribe it. I will have a hunt later to see if I still have some and can tell you the name. Not sure if its suitable for a 7 mth old but you can always check.

I don't have any other new suggestions I'm afraid, other than seeing a dermatologist if you haven't already?