Is this a milk allergy?

Hi ladies, I've been lurking on this board but have never posted. I'm hoping someone has some words of wisdom/experience! 

My DD is 2 months old and I EBF. About 2 weeks ago, I noticed that her BMs were mucus-y and VERY green. The pedi said that it could be a virus, but potentially a dairy allergy, and told me to go off dairy to see if that improved things. She took stool samples and they've come back as negative for a virus or parasite. 

Problem is, DD is still having the mucus. It has improved and her BMs are back to yellow, but there is definitely still mucus. I cut out all obvious sources of dairy, but I have had chocolate and also accidentally ate a piece of cheese at a friend's house over the weekend (I got really excited by the manchego and just completely forgot for a minute lol). So, I'm assuming that those transgressions could explain why I've seen an improvement, but not total back to normal BMs, right?

I haven't talked to the pedi again (we're trading phone messages), but she did want to know if the mucus remained. In the meantime, does this sound like a dairy allergy? DD's other symptoms are extreme gassiness and discomfort. The skin around her right eye will also get red and irritated for seemingly no reason, and she sneezes frequently, although I don't know if those things are connected. She does NOT have eczema, rash, hives, or visible blood in the stool.

Oh - and I should also mention that she has started drooling a LOT lately. I've read that excessive drooling can explain mucus in the diapers, but the pedi has not mentioned this to me. I plan on bringing it up when we speak.

Thanks and SORRY this is so long!