I have the same problem in my family too, my eldest daughter is fine, no problems other than a bit of eczema every now and then but my 10 month old is a nightmare, she seems to have everything .... eczema, asthma, hayfever, dairy allergy ..... I have done the same thing with both my children and fed them the same to start with but still seemed to have problems with the baby! I do know that these problems have got a lot better since she has been on a dairy free diet but it is not something that I did without countless visits to the doctor and a referral to the hospital.
My youngest has only recently come down with hayfever and someone recommended giving a teaspoon of honey every day that ha been made in the area you live in??? Something to do with the honey being made with the pollen the child is allergic to! Yet to try it but am definitely going to, anything to stop using an antihistamine every day.
Not sure if this will help at all but at least you will know you are not the only one with the same problem!