I'm not sure about the allergy thing here. My child was severly allergic to dairy as an infant and it would not stay down long - then projectile vomiting and hives. There is a lot of stuff in OTC cold meds that could cause a reaction. That being said, try other comfort measures and skip the meds. Saline nasal spray and suction bulb, baby vicks, weak sweetened lukewarm decaf mint tea.
My son (3) got really sick this past fall, when he had a bad cold and I was trying to get OTC cough meds into him because he coughed and coughed and couldn't eat, sleep, drink. EVERY time I gave him the meds and he would throw them right back up. I'd never had that problem as he was on liquid Zyrtec for summer allergies. By the next morning his breathing was really congested and I rushed him to the doctor. In this case, his respiratory tissue in the bronchial tubes had become infected because the continuous coughing had it so irritated. The doctor could not understand that I hadn't gotten cough medicine in him and I told him, I DID, but he can't keep it down and that is why we are here! In this case the doctor said it was because his little tummy was empty and the meds irritated it. So, he gave him some shots, anti-inflammatory and I think something for nausea, and antihistamine. That calmed things down enough that I could get food into him and start the OTC meds.
I hope you quickly find out what is going on.