Curves!
In my testing whole wheat bread doesn't behave much better than white bread. My BGs shoot straight up, within 15 minutes. I try to pre-bolus anyway, but it is imperative with something like a bagel.
Bagels are also very high in carbs. I'd have to read the label, but one is prolly like 3 or 4 slices of bread.
You don't mention breakfast. If you skip it, that can cause lunchtime spikes too. I've tested that enough
Try picking a standard lunch and test it every hour or half hour to build a fuller profile. Then plot it on a graph. Now try things to make the graph flatter: pre-bolus, lower GI, and less carbs. It's a worthwhile exercise.
