Yes I think you are very right to be concerned. It is possible that the excess drainage is making it into his stomach and that is what he is spitting up. He can't "spit up" from his lungs. If he is coughing up mucous, it is hard to tell where it is coming from: his nose or his lungs. You can gently syringe his nose before you feed him and you can syringe his mouth and nose every time he seems to be choking or snorting too much to breathe. Letting him sleep in his car seat will help too.
Babies that small usually don't have allergies like adults do or asthma. Asthma in babies is too difficult to diagnose because it is difficult to tell how well their lungs are supposed to be functioning with the various tests they have for asthma.
The symptoms your baby is experiencing can have so many other causes. I would put Allergies and asthma far down on the list and RSV or some sort of infection closer to the top.
It is possible that the rash is unrelated and just a case of eczema. Is she feeding him formula? Perhaps he is also lactose intolerant. In this case, changing formulas would get rid of some of the excess fluid build up. I have also found that milk and milk based formula can cause eczema.
Trust your instincts. If the baby seems lethargic and stops eating and loses intrest in his feedings, then it is really time to call the doctor. If he is losing color or not breathing, call the ER right away.
I hope the baby gets better soon so that the both of you can enjoy him