Cat Scans and Post Covid follow-up

I have recently had Covid 19 ...again.. and this time secondary infections, one being pneumonia. I was treated according to medical standards to date and needed further antibiotics following a bladder infection. I have had two chest x rays with the last noting cleared of pneumonia, although being down this road before, knowing it can change. I am experiencing a throb in the upper thoracic back posterior, that is really tight. Periodically I feel a very heavy tightness in the chest area again mostly left side. This is aside from the soreness and dizziness I experience after a cough (short or long duration). At present I am thinking it could just be irritation from all of the above. I am curious if a CAT scan of the lungs will pick up more than an x-ray. I do know it can assist in looking at the heart and any abnormalities associated from the pneumonia that were present during pneumonia. If this were pulmonary circulation- related would it pick up anything missing that an x-ray might not detect?