It's possible and I guess if the doc says she thinks it's allergic then you may need to with that until you can think otherwise. One of the things with dairy is that the exposure will build just like you describe - reactions to allergen increasing with exposure.
I was not dairy or egg free while breast feeding DS1 (his allergies were diagnosed through direct exposure at 10 months and 1 year) but looking back he did have dry skin and unexplained welts and rashes which could possibly have been a reaction to increased exposure through the milk
Did she suggest some anti histamine or creams to calm the itching? Hopefully she gets better soon.
Temp might indicate viral so you never know, it may just be viral.
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DS1 Feb 02; DS2 Oct 04; DS3 June 07
Food & environmental allergies, eczema,
anaphylaxis, hayfever, food chemical intolerance and asthma.
Treat the earth well: it was not given to you by your parents,
it was loaned to you by your children. ~ Ancient Indian Proverb