This child is meant to be here and you are meant to be her mother! I'm so sorry you are going though this. I will say to you that we bf and had huge issues with eczema!! I also am conflicted about feeling like I passed on my leaky gut to DS. Believe me, as mothers, there is NO shortage of guilt regardless of what you do.
There are a number of issues you should consider in addition to the "allergenic" profile of what your child is eating.
I would definately recommend against any lipid formula. The DHA in formula is engineered from fungus and microalgae, it is not natural fats, and NOTHING like BM regardless of what their ads claim.
See info below about fortification protocol. I feel very strongly that infants need cholesterol and essential fatty acids for proper brain development, but in a natural form, not manufactured. But of course,they are also critical for eczema sufferers who have messed up lipid profiles to begin with.
I wonder if the engineered omega 3 fatty acids in the lipid formulas act like the similarly lab created "hydrogenated fats"... in that they also block the body's synthesis and utilization of real fatty acids and in fact can cause eczema (trans fats are really bad for eczema sufferers for this reason).
But that is my own personal theory. Nonetheless, there is a lot of evidence that the lipid formulas have been creating a great deal of problems.
Also, you should start a probiotic supplement. There is mainstream research being done on this right now, and the next wave of "fabulous, new and improved" formula will be with probiotics added. Ok, so that was a snide way of saying that it is critically important. Especially since you notice the gut/immune system dysfunction, eczema.
has a number of studies posted on their website regarding eczema and babies. Baby Jarrodophilus, in refrigerated case at health food stores is also very good. You might want to try both the Jarrow and the Culturelle, as Culturelle (lactobacillus GG) is a helper probiotic.. it doesn't colonize the gut forever, only as you are taking it, but it helps the other probiotics (like the natural organisms in Jarrow that are isolated from healthy babies' intestines) take hold. That is what my naturopath recommended.
I agree with you, I would do everything possible to be sure my baby never ever got soy formula.
Formula fortification protocol for essential fats:
Humans (and baby humans too!) need omega 3 fats (and not engineered ones!)
See below on this page for fortifying commercial formulas
This page and links below will change your mind about DHA formulas: