What is your "bedtime injection"? I'm assuming you mean your basal insulin, if that's the case, carb counting isn't required to calculate your basal dose. Most people are on fairly consistent dosed of basal insulin, although they might change the dose of the consider it isn't working for them - I.e it's not keeping them stable overnight.
You say you don't eat carbs, but drink coke. You might want to check the carb content of the coke and check whether it has an impact on your blood sugar levels to think about whether you need to bolus for it.
Have you actually been on a carb counting course?