Mama to DD 2.18.03, DS 3.18.06, DD 5.7.11
Though I don't know for sure..... I think the connection is more that someone who is allergic to one thing, especially at so young an age, is likely to be allergic to other things as well. My daughter has had a severe dairy allergy since about 3 mo, but beef is thankfully something she can have with no trouble. Beef is usually included in allergy tests for toddlers because it is a common allergen.
You didn't say how long you have been without dairy. If it hasn't been too long, it is possible that the first days or weeks seemed good without the main allergen, but now that that's gone she could be noticing something else that has been in there all along. I say this because as an allergic person myself once I got rid of the big allergens I started to notice other symptoms that had been drowned out. (How did I ever miss all this?) Now, with my corn allergy, I even reconsider eating something with xanthum gum as the last ingredient on the list! The clearer my body gets (I'm allergic to a lot!) the more I notice when something creeps in.
I still agree with your guess about the steak being the likely culprit, but I mention this just as a possibility to consider.
Give me a few minutes while I caffeinate.
I think it's something like less than 5%-10% are allergic to both. Are you keeping a food log? Maybe give it some time and try beef again? I think when they are that young it is easiest to find "issues" with a really detailed food log.