Ear infections, congestion, daycare or a dairy allergy...insight please!!!

Okay so I started my daughter on cows milk in mid Oct-Nov. I noticed she was starting to get some eczema in spots. But I just assumed it was maybe because of our horrible cold weather in Pennsylvania. But maybe dairy allergy?? Anyways, I got her in a daycare around March. She has had 4-5 ear infections since starting daycare, and I’ve noticed it all starts as congestion and runny nose, then I assume it drains to the ears and then we deal with another ear infection. It is now June, and I think we MAY have another ear infection! Side note: every time I take her to the dr they say “well she still has fluid there but it’s no longer infected” sooooo... does this mean that she’s always going to be set up for an ear infection if we still have fluid there?! My question is...is this just a result of a cold from being in daycare or could this be an underlying dairy allergy? She didn’t have any issues going to milk from Oct-Jan. And just noticed the eczema in Feb. Could it take that long to notice an allergy? Or should I see more signs from a milk allergy!?