Thanks for your question.
It is a pleasure knowing that you are doing physical activities well and on a healthy diet. Anyway, irregular blood sugar levels are associated with high blood glucose (sugar) levels. Moreover, researches show that this happens more in teenagers. This is due to the hormonal changes occurring in your body while you are on your periods. Due to higher glucose levels in blood, need of insulin also increases. Making things a little worse, having type 1 diabetes can affect your entire menstrual cycle also.
I would like to suggest you to see your doctor for more information and help. Tell him about your monthly sugar level fluctuations. He will be able to explain how the monthly hormonal changes affect your diabetes management. After a close monitoring of glucose levels in the time of your periods, your doctor will help adjusting insulin for coming months. By the time, you will be well aware of how your insulin needs changes with your menstrual cycle. During the time of monitoring, you should maintain a balanced diet plan also to contribute in sugar control. Your concern about weight maintaining will also help you in achieving greater results in no time.
Test your glucose levels at around 2.00 and 3.00 am to know more about rebound hyperglycemia, which is also called Somogyi effect. Low blood sugar levels are what causing this effect.
Stay healthy and young. Good luck.