Could be bronchitis, because you will feel very tight in the chest. Normally it would be accompanied by a pretty painful cough and phlegm. It could also be pneumonia, since you aren't actually coughing anything up. Sometimes pneumonia congestion can be so deep that it is impossible to actually cough it up and it tears up your lungs instead.

It is possible that your post nasal drip is just going straight to your lungs and filling them, or you could have a lung infection that isn't sinus related, or both.

You should have a doctor to check you out to make sure you don't have either of these conditions. Pneumonia can be swift and deadly.