I assume the “just in case” being refered to is lung cancer or TB. I had asthma return after nearly 40 years without a severe attack earlier this year, they gave me a chest X-ray “just in case” but as the doc said, it’s unlikely to be TB and if it’s cancer it’s already too late. Coughing up blood when you’ve had a cough for three weeks is no more serious than what’s causing the cough which is as yet unknown. A doc seeing you in real life will check a few simple things we can’t on line, not even DrP.
Edit: if they do give you a chest X-ray dig out any old ones you have lying around even they don’t cover all the lungs, they told me that interpreting chest x-rays without old ones to compare is really hard.