Getting over a cold, now with tightness in chest with a dry cough. what can i do?

Reactive airways : It is very likely tht the infection could have triggered bronchial hyper-reactivity. Asthma can also present in a similar fashion. Please talk to your doctor to see if you need an rescue inhaler and potentially long acting medications for atleast 3 months . Medications are usually titrated every 3 months in this case

See your doctor: Having recurring illness is troubling. In order to achieve a specific and correct doagnosis with symptoms like this, you'll need to visit your doctor. Only after a face-to-face evaluation will he/she be able to properly diagnose and treat you.