How does a chest cold or respiratory infection impact blood test results?

Patient: Hello Doctor. I recently went to my doctor for my annual physical and at the time of my visit I had a very bad cold and chest congestion. A crackling noise in my chest with a lot of mucus. I was and still am using my asthma puffers due to the shortness of breath I experience at times. It has been 1 week and my congestion seems to be getting better. During the physical my Doctor had me do routine blood tests. The blood test results showed a higher than normal red blood cell count. The doctor told me to re do the test when I was over my cold as this could have impacted the results. Does this all make sense? Is it normal to have an increased red blood cell count during a chest and lung infection orcold? What else could of been impacted in the blood test results as a result of me being sick?