Best to ask your friendly pharmacist before taking anything.
Although assuming you are type 1...? You may have more leeway with carb intake.
as an example, when i catch something, I reach for the Night Nurse capsules. They have no carbs and work well for me so I can get a good night’s sleep.
In contrast, the Night Nurse syrup has sugars in it, so I avoid.
There’s a vast difference between a cold and real flu, and the flu jab only works on some of the flu strains around on any given year, so it is no guarantee you won’t come down with real flu.
Take care of yourself, and check with the pharmacist. They are the experts.