I would definitely use TA1 or Thymulin in this case. There is evidence showing semaglutide ammeliorates LPS induced lung injury and can decrease pulmonary inflammation. This is an animal model of study, but given the safety profile I would not hesitate to start using it. Could consider GHK-CU for similar reasons.
Look at the gut also. There is emerging evidence there is a gut-lung axis influencing pulmonary conditions. Remediation of microbiota with prebiotics such as low dose lactulose would be reasonable to consider, especially given high dose antibiotics.
I cant link resources but can share if needed.
Clyde Boswell