I have eczema and have had this at times, it’s a bugger but it does go. I would -
Think of anything that’s different since the baby - baby creams, washing powders, baby powder, and change it. If you’ve had the heating up, try humidifiers next winter.
Pay for a private derm appt if you can. GPS just aren’t v clued up, the NHS wait is ages, and often a derm will sort it out pretty instantly
Use Dermol 500 as a gentle antibacterial handwash. Stay away from hot or v cold water.
Use cotton or bamboo gloves overnight - really helps cream sink in. You can get them in packs of 10 from Amazon.
The creams I find are good are O Keefes especially the overnight one, L’occitaine 25% Shea butter (but £££), people say that body shop hemp is a good dupe of the Shea butter, also La Roche Posays Lipikar cream is great as body lotion so worth seeing if they have a hand cream. You have to be persistent, because different things work for different people. Generally the cheap aqueous type creams are petroleum jelly based and useless. The gloves will always help.
I will go don’t worry.