The spikes you mention are a bit unusual given you mention the significant drop in HbA1c and these numbers do indicate that your suspicion is right. The spike to 18.2 after breakfast if it had high crabs, I think is still a bit on the higher side although you haven't mentioned what it was before the breakfast because if due to dawn phenomenon if BG was already say 12 and then you had high carb breakfast I wouldn't be so surprised that it went to 18.2 - that has happened with me in the initial days of experimenting with food where it went from 9 to 14.1 after I had coffee made with Oat Milk and 3 toasts of sourdough bread with butter. The spike from 5.5 to 12.5 at lunch time seems bit high too if the lunch was low carb but if high carb it would not be so surprising.