Brief Answer:
Need more information.

Detailed Answer:
Hi, thanks for the query.
Myself Dr Karade ENT Specialist.
Sinus infection can cause lower respiratory track infection which can result in shortness of breath and a tight chest .
Since you don't have drainage , i like to know whether you are having post nasal drainage back in throat , sneezing , cough dry or with sputum , history of allergy , asthma .
I would advice you use Steam Inhalation , Antihistaminic + Leukotriene antagonists combination to get relief .
If you don’t get relief , ENT examination & investigation become essential.
If you have any further questions I will be happy to help.
Regards.

---

Brief Answer:
It is more likely due to sinuses infection.

Detailed Answer:
Hi ,
Thanks for follow up query.
Ultimately sinuses going to drain into lower respiratory track due to gravity . Also humidification of breathing air takes place into sinuses then it goes to lung.
So sinuses infection can cause lower respiratory track infection which can result in shortness of breath and a tight chest . Your shortness of breath and a tight chest is more likely due to sinuses infection than just viral.
I would advice you use Steam Inhalation , Antihistaminic + Leukotriene antagonists combination & saline nasal drop to get relief .
If relief is not upto satisfaction level then consultation with your ENT doctor will become essential.
Thanks & Regards.

---