D-dimer results higher when sick with a cold?

Possible: D dimer can be increased in infections. Sepsis. Inflammation. And in thromboembolic disease. So it helps to rule out blood clot when it is negative. Being positive is less conclusive. So if someone has cold / pneumonia rarely it could be elevated.

Depends: D dimer goes up in blood clots anywhere and in inflammation. Simple cold unlikely will do it, but cold is used so loosely that other inflammatory problems can be the cause.