Yes, infection does cause blood sugars to be higher than they would be otherwise. If you are no taking insulin, then there's not much you can do to reduce blood glucose levels. Keeping hydrated, by drinking non sugary drinks is important. Unless taking insulin, then not eating much for a few hours or couple of days doesn't matter too much. If taking tablets, then check the patient information leaflet in the pack for advice about what to do if unwell - or ask GP / pharmacist / NHS telephone advice service etc for advice, by phone / email / face to face.
If infection is caused by bacteria, then antibiotics to fight infection will help to bring blood sugar levels nearer normal. If it's caused by a virus eg a cold, then antibiotics won't help. For some infections, eg flu or shingles, there are specific anti-viral medications that can help, but only if you start them early enough, so you need to make contact with someone who can diagnose and prescribe as early as possible, if you suspect that's what you havee.