Whether you agree with the Covid jabs or not, it might be a good idea to look into the two available pneumonia vaccines if you are eligible. I got the Pneumovax 23 last year as a precaution.
I doubt they would give it with one being sick. Increased risks.
That is one of the problems now. Doing vaxes in a pandemic is a big medical no no for the viroligists and immunologists in the know.