Why would someone be experiencing chest tightening along with a constant throat irritation? especially if it isn't a sinus infection?

Asthma or gerd: These symptoms are fairly nonspecific and could be caused by muliple conditions. allergies with reactive airway disease(asthma) is a considerstion. In addition gastroesophageal reflux often manifests with these types of symptoms rather than classic heartburn. These symptoms would be laryngopharyngeal reflux(lpr) and may improve with antireflux meds. See a doctor for further workup