Yes, but mine was a bit atypical. At about 6 months I switched to formula - my son a guzzler only took 1 ounce and within a few minutes has small dots around his mouth. They went away quickly at least.
After speaking with the doctor, he went on soy formula and did fine. I gave him soy yogurt and cheese as well. I slowly switched to soy milk - using the Enfamil next steps to transition as I found it more portable than soy milk since it is a solid and found Target clearancing out a large stock.
Just tread lightly with food that may contain milk. Find out recommended dosage of Benadryl or whatever your ped recommends and keep a bottle and dispenser with you always! Gives you peace of mind.
I found over time that he could eat yogurt and cheese fine, but kept him on soy milk until he was close to 3. I also found that he'd gave the same little dots as he got older if he ate certain fruit snacks and things (may have been dye related), but we could never figure out what it was - so we made sure to stick natural foods as best we could and monitor the processed foods he ate.
I had the allergy blood test done at a year that did NOT show a milk allergy (yet he got the dots still). At an allergist had the scratch test done on his back at 2 and again showed NO reaction. At 5, I took him to an allergist again as he had gotten hives from what we thought was bananas as an infant and checked the milk again. NO reaction bananas or milk. So I don't put a lot of stock in the test which showed some reaction to foods he ate without incidence on a regular basis.
He is 6 and drinks skim milk (though not a huge milk fan), eats yogurt & cheese regularly and even some bananas now - that took me the longest to do. The allergist said the hives he had as an infant may have been a virus, but she did not think it was a reaction to bananas.
The bottom line though is food avoidance is best as children can outgrow many food allergies (not likely with nuts though). Wait it out until close to 3 and also make sure you wait to introduce foods until recommended time since once there is one allergy there could be more. Be vigilant with nuts and watch the baby fruits since many have combos with berries which my ped said stay away from until at least a year by which time I was pretty much done with baby food.