Do glucose levels rise if you have an infection?

Yes: Any physiological stress can raise your blood sugar. That would include infections, trauma, burns, surgery, acute events such as heart attacks and strokes or exacerbations of chronic medical problems.

Possibly: For diabetics in particular the stress and increased metabolic demands due to an infection will result in a rise in blood glucose as you convert glycogen and other stores of energy to glucose but cannot then utilize it. As a general phenomenon in non-diabetics, the same can be seen as part of the cortisol-driven stress response, which can be brought on by severe illness, including infection.