Could my two month old have a milk allergy?

My two month old son has been congested since he was two weeks old. I've brought him to the doc a few times and they haven't really helped much. He spits up alot and has diarrhea,I feed him 90% of the time. He'll have maybe 8 oz of formula each day. Could he have a milk allergy? I thought about eliminating dairy and trying Nutamigen for a few days. If I try the Nutramigen how soon will I see a difference in his symptoms? Thanks!