Don't know. You live in VA, I'd say 2-8000 IU during the summer depending on your reaction.

Supplementing with vitamin D is perfectly safe during breastfeeding, in fact, it's how the baby receives vitamin D so the mother's levels need to be high. In fact in Norway and Sweden breastfeeding babies are recommended to be supplemented with 1,000 IU of vitamin D per day via drops. Before the sun scare, the recommendation used to be 2,000 IU per day.

So remember when you have multiple symptoms of vitamin D deficiency you need to supplement with 7-12k per day for 3 months. It doesn't matter if it moves into summer, obviously in the past the sun exposure alone wasn't enough and won't be enough now to address the deficiencies. And your required level of vitamin D supplementation doesn't depend on one symptom, i.e., eczema but the alleviation of them all. You'll notice different improvements at different rates and they're progressive.

Eczema naturally improves with the summer due to the increased vitamin D. So find the level that starts the healing now. Take note of other healing symptoms. As you sun more, and your deficiency symptoms improve more, find the level between supplements and sun exposure that keeps your skin completely healed, soft and supple. Move it up and down as necessary.

And remember you need enough to fill the deficiency, maintain current health status once fixed, and build some stores for winter. That could take a lot of supplementation/exposure.

Also for eczema--coconut oil with or without OOO mixed in.