In the Guardian article in the parent comment, the warning says that any anti-inflammatory drug may be a risk, not just NSAIDs. They include cortisone as an example of a drug to avoid, which is a non-NSAID anti-inflammatory.
I think it's generally the case that taking pain killers isn't a fantastic idea when you have an infection. Of course, for mild infections there's little consequence, but in this case it might be best to avoid them. Just wrap up warm and stay hydrated.
