Can I have a cold and pneumonia at the same time?

[Isabelly97]

Long story short: I am on day 8 of a zpak for pneumonia (I still have the cough), and today I woke up with a sore throat, a runny nose, and now I keep sneezing like I have a cold. Is it possible to have a cold and lingering pneumonia at the same time?

Actual Long Story with all the details:
About two months ago, I had a cold that hung around and turned into pneumonia two weeks ago. I knew it was pneumonia (I've had it before) but my first doctor didn't agree and since it was at my school's health center, there was no way to take an x-ray. I went to another doctor when I had the chance, about a week later, who was able to take an x-ray and say for sure it was pneumonia. I was put on a z-pak, prednisone for a sore rib/muscle from coughing, and an inhaler and delsym for the cough. The zpak was the kind where I took a pill for five days, but it would last for ten days, and I'm on day 8 and I still have the same cough I had before (muscle pain too, the prednisone didn't seem to help but that's not the problem). Now I have a runny nose, a sore/tickle-y throat, and I keep sneezing like I have a cold. I also sort of felt a rattle in my lung on the opposite side of where my pneumonia started, but I'm scared to admit that. I don't want pneumonia anymore!

Can I really be getting a cold while I still have pneumonia??