Blood Sugars and the cold

If you are unwell, your body will release glucose into your blood stream to help you fight off the lurgy.
If your pancreas was behaving itself, it would release extra insulin to use this extra glucose. Unfortunately, our pancreases (pancreai?) are misbehaving so we have to inject the insulin.
When feeling ill, I usually increase my basal. However, this is a slightly risky option as it requires me to spot when I am feeling better and I stop releasing that extra glucose.
A safer option maybe to do more bolus corrections (with care not to double bolus when you have insulin on board). However, this would mean you are not able to do any top ups when you are asleep.

A compromise may be a small basal increase and less bolus correction top ups.

Whichever way you go, do lots of testing when you are unwell ... and drink plenty of liquids.

I hope you feel better soon.

I just correct with short acting insulin I don't increase the basal (which would probably work too, but I don't want too many "moving parts"). I also check more often.