It is possible that you developed the eczema and hair loss repeatedly due to the stress of detoxing, all B vitamins (as well as several other nutrients...) are consumed in large quantities during any stress and a deficiency of a number of them will cause hairloss as well as eczema, for this last one particularly Vit. B 6 comes to mind. Lack of iodine could also be related to hair loss and dry eyes. A dry and itchy scalp could be a sign of lack of essential fatty acids, unless there's a visible rash, dandruff or any type of lesions, in which case it could be a number of things, (including a fungal infection, which can thrive when we lack B vitamins). Be sure also to get zinc-rich foods, not too easy to do, so you may want to add a supplement.
One thing I've found very effective for myself on more than one occasion when I was losing hair due to hypothyroidism and/or adrenal fatigue/stress, is silica plus MSM, they come together in very affordable caplets, "KAL" brand, it's called Super Silica Plus with MSM. Silica is also cleansing, most people notice the need to go #2 more often, but that to me was definitely a plus because I was suffereing from constipation at the time.
Not sure... I did help my best friend stop her hair loss many years ago with B-complex, she wasn't eating well and was always on the run so it was kind of easy for me to tell. And I did share in a PM with the OP something else that I know works for many, so let me know.