Food Allergies Treatment

I’ve been slowly introducing cow’s milk to my 1-year old daughter. Recently she has been having diarrhea and developed a minor rash on her face. Is this evidence of a cow-milk allergy? What are some other symptoms?
What do people do when their babies are allergic to cow’s milk? Feed soy milk?
Thank you.

Since my daughter is now 1 I have begun to try to introduce cow’s milk. However, after about 10 minutes of giving it to her she starts coughing and getting very congested and has a mucusy wheezing. If I give her benedryl it goes away in a few hours. But, once I give her the milk it comes back. I don’t understand because she drinks milk-based formula, and she also had a skin allergy test done and it showed that she was not allergic to milk. What is happening here?