My older son is 3 yrs, 2 months and we found he was allergic to dairy at 6 months and egg at about a year old. He has never had any tests, but is now still quite strongly allergic to dairy and maybe less so to egg (?). So, like you, I was a bit cautious and on the lookout for similar issues with J. I really really wanted him to not be allergic, so I was in denial for a bit, but at around 5 weeks old I came to the conclusion that dairy in my diet did seem to affect him. He was a very sicky baby, just like A, and, although not very definitively, avoiding dairy in my diet seemed to make this better. He never had eczema though, whereas A did from about 3 months. (I wasn't avoiding dairy until 6 months with him as I had no idea).
I wasn't overly strict with myself with the dairy avoidance with J (couldn't stop eating chocolate!) but I did my best

. I did the milk dab on the cheek test once at about 4 months, and again at about 5 months and both times there was no reaction at all. And at 5 months I reintroduced dairy into my diet with no effect to him. Yay!!
I started giving him small amounts of dairy foods at about 8 months (just some cheese every now and again), and then gradually introduced a bit more (yoghurt). No reaction!!! Yay yay yay!! He's also fine with egg. I've only given him actual milk in cereal a few times, but that's really only to avoid exposing A to it, as it's quite hard to contain the mess! He is fine with that too though.
So yes, I believe that J may have had a mild dairy allergy or just an intolerance and grew out of it by around 5 months of age. I'd say this could've happened with your daughter too.
I think I'd probably do as you say, and reintroduce dairy into your diet and see if it has any effect. You could start of gradually with milk in your tea, occasional chocolate or whatever and then if she seems fine, go for it

!
Not sure what you could do about the egg, but based on your experience with your son I might be a bit more cautious with that. I think it's a bit harder to do the dab test with egg too.