Yes, milk definitely does increase mucous production in some babies. My oldest would get congested everytime she drank milk when she was an infant. She was on breastmilk for 7 months, then soy until 15 months. Even after she was on whole milk, whenever she was sick, I’d go back to soy because the congestion was so bad. She doesn’t have any problems with milk now, so she did outgrow this, and my other two don’t get congested from milk at all.
I’d try the soy until she’s feeling better. I don’t know about Pediasure….I’ve heard it’s lactose free, but I think it does contain milk protein. Rice milk is another alternative, but it can be binding.
Good luck and I hope she’s feeling better soon.