Can a Cows Milk Allergy start at toddler stage?

Hey, I just wondered if anyone else's little one started an allergy to Milk when they around the age of 2?
My daughter has a persistent cough, it's worsens at nap time and through the night but she also has it on and off through the day. We where told by our GP this could possibly be asthma which they won't test for till she's older. She has an inhaler which sometimes helps but sometimes doesn't. But lately we have noticed she sounds bunged up also, which sounds like it could be causing the cough. Someone I know mentioned it could be a Milk allergy, however we both agreed this is normally starts from when there smaller and also includes stomach issues which I don't think my little one suffers with. Her poos are normally solid.

Does anyone else's little one have a milk/dairy allergy that started when they where 2?

Thanks in Advance

1