4 yr old has allergies but vomits due to phlegm buildup

He seemed to get cold like symptoms every couple of months. Red, watery eyes, runny or stopped up nose, ALWAYS has a cough. We used to treat it as a cold and have used all the cold medicines and our first Dr. said to give him an extended long-lasting cough syrup (didn't work), vicks vapour rub, the patches, steam - you name it. Nothing seemed to help the cough. And he would always end up vomitting. Our new Dr. took one look and said it was allergies and to give him the Zyrtec, as needed. The bouts usually last about two weeks from start to finish and the Zyrtec seems to help a little with the rest of the symptoms but not the cough. He also coughs more when hot. He had croup one time when he was little. I just don't want this to go too long and turn into some type of asthma. I am allergic to cats and dogs, dust mites, some grasses and cottonwoods. My husband has no allergies to my knowledge but was born with a cleft lip and palet.

The little guy has always had an issue with vomitting. He will have like a coughing fit and then vomits. This also happens when he is really upset and crying really hard he will vomit. Like he has a quick gag reflex.
When he is sleeping and if it gets warm in the room he will get to coughing. I try to keep him cool and his head a bit elevated when he is sleeping.
He has been having these cold like symptoms at least since he was 12 months of age. I have asked and asked about my son having allergies and my original Dr. said kids could not have allergies at that age.