system
Given the following post, respond as if you're commenting on Reddit:
human
If I accidentally cut or graze my finger and I also have a cold or the flu, am I more likely to suffer an infection in the wound because my immune system is already being challenged elsewhere?

I wonder whether having one relatively manageable infection prevents you from mounting a sufficient response to another, different kind of infection. I understand that different parts of the white blood cell roster may be involved, but in terms of complement and other factors, how much is my body's innate immune response affected by multiple infections.
gpt
Unless you are immunologically compromised or deficient then you are not likely to suffer an additional infection. Your body's innate immune system recognizes specific molecular patterns on bacterial cells that are not present at all in eukaryotic cells which is why it can respond so quickly but with non-specificity while your adaptive immune system recognizes specific antigens and mounts a very controlled response which takes a few hours-days. If you already have a cold or flu your adaptive immune cells would be the ones fighting it. Of course your innate immune cells would probably also contribute somewhat but they would be free to start staging a response at the new site of injury while the adaptive response catches up. 

TL;DR...No you are not more likely to suffer an infection if you get cut while already sick.