Eczema and psoriasis are genetic and can be passed down. Psoriasis is an autoimmune disorder but certain types of psoriasis can be exacerbated by environmental factors such as smoking. Eczema is more likely to be exacerbated by environmental factors like allergies to pollen and food allergies, exposure to chemicals and fragrances, and changes in the weather.
I would take your baby to a pediatric dermatologist. It sounds like he has baby eczema; some children outgrow it. Yours might be caused by pregnancy hormones but you should go to a dermatologist too. Maybe you can schedule an appointment together.
Edited to say: Yes, the poster above who said that asthma and eczema are related is correct; also, the poster who mentioned Aquaphor is right on track. I used to work for a dermatologist and Aquaphor is definitely what she recommended as an OTC for eczema.