I'm sure that doctors want to be very cautious about handing out antibiotics, especially if they haven't seen you in person recently to be sure you really need them. We were going on a 5-wk trip, and I had had an issue earlier where I should have taken antibiotics, so my doc decided that he could trust that I would know the symptoms of a flair-up and would only use the antibiotics if necessary. Thankfully, I didn't have any such issue on our trip.

What he prescribed is Amoxicillin 250mg

It's a frustration of mine as well, how long it takes the pulmonologist to get back to me. Your PCP might be faster, but I was able to go to a walk in clinic and get antibiotics when I was personally confident that the same bacterial infection had returned. I kept getting the same bug 4 times in a row. There are different antibiotics for different bugs, so you might want to get a sputum test if you're not confident to be sure that you get the right antibiotic. I was also able to get a sputum test at the walk-in clinic, but it takes at least 3 days for results. I'm on low dose antibiotics all the time now. The last cold and severe lung congestion I got was from a virus and unfortunately they are not responsive to antibiotics. I definitely suggest taking some action. I suspect my weeks long patience, caused my lungs harm in the mean time.