Is it normal to feel dizzy and faint when you have a bad cold?

I've had a bad cold with a runny nose, headaches, low grade fever and periodically cough up phlegm. It's one of the worst colds I've had because I've also had chills but it's not strep or the flu because I went to the doctor to see if it was. I just have a question regarding feeling dizzy and faint. I've felt this way since a few days ago but it's really bad. I have to sit down after a short time or I feel like I'm gonna drop. Is this normal or should I be concerned? Thank you!