Just wanted to second the recommendation to RESEARCH the meds you are prescribed-- I had one of the worst cases of eczema my dermatologist had ever seen on my hands & legs after giving birth last spring (like you, I've had it for years, but it got much worse during pregnancy, & MUCH worse after giving birth). He prescribed a few things-- one was a cortisone cream, which helped at first, but eventually thinned my skin and made it harder to heal. Later, he prescribed protopic, which is not recommended for nursing, since it is an immune suppressant. I don't know if he forgot I was nursing between appointments or what, but I am really glad I read the info.
In the end, I relied on a natural salve that I make myself, and by the 3-4 month mark, the eczema began to subside. I am convinced that mine was largely hormonal, and it made sense when I found out that prolactin and other hormones begin to level out around 3-4 months. Like magic, that's when my symptoms started improving.
Hope your situation improves soon-- I know how miserable it is. For me, it was the worst part of pregnancy & early motherhood-- I didn't mind the sleepless nights or constant nursing, I just wished I could do the dishes or wash my hair without inviting agony. That said, there is no way I would have given up nursing to take a medication for eczema. It was bad. Very bad. But I also believe that the fact I was fed some formula from 3 months on could have contributed to me having eczema, and if there is any way for me to spare DD from having eczema, it is BF'ing.
Good luck! Hope you find the treatment that's right for you!