4 moth old baby and eczema

Dear Doctors,

I am a distressed mom of a 4 month old baby boy. When he was 1 month old he developed very dry and itchy skin, later rash all over his body that we were told is eczema.
After trying diffrent creams we consulted the local homeopath. I never applied creams with steroids he was prescribed though, being too cautious of side effects. THe homeopath gave him Psorium, he did not react much to it; was still very itchy at nights, with very flaky skin even though i was applying masses of moisturising creams. Week after he was given Suphur 30, to which he responded with outbreak of big spots, and patches of red skin that weep.Other parts of his skin seem gone softer. Meanwhile I, myself has got very bad cold and was drinking different cold medicines. Now his itchiness came back and he can't stop scratching them. Do you know whether cold/sore throat medicines can pass through breast milk and effect my child's eczema? I was having antibiotics soon before and after the delivery of this baby as had bad chest infection, thinking that it maybe the cause of his eczema. Are we on the right way? please advise

thank you,
gulnara