Can a fractured rib cause pneumonia?

I was reading online that a broken or fractured rib can cause pneumonia, i don't want to go to the hospital because i know they can't really do nothing about a broken rib. I'm doing everything in my power to take deep breaths and cough every now and then to avoid getting pneumonia even tho it hurts, the pain isn't that bad as it was the first and second day (i'm on my third day). Can an injured rib also cause dizziness? I'm not getting any fevers, or vommitting or any other stuff, just dizziness. Thanks in advance! Might i add that i fell down 3 or 4 stairs.