Yes it is normal and you actually have a very low body weight too, also 1000-1600 calories a day is nothing, you need far more than that as your average daily intake anyway.
Hormonal changes can and do cause an increase in appetite and cravings but if you are not eating enough on a regular basis then it's going to make those cravings worse and your hunger even more intense, I am anorexic, I eat around 1000 calories a day and because it's nearly killed me twice if my weight starts to dip I know I have to do something to stop myself from going underweight again, I will eat a sandwich and then still be hungry and eat a huge amount of food, if I was able to eat more on a regular basis then that wouldn't happen as much, it's a basic consequence of malnourishment and suppressing your natural body weight.
The chances are that you are not eating enough fats and carbs etc through the rest of the month so when your period comes and the hormones spike your hunger your body responds by wanting even more, I used to always want a little more than usual but since my eating disorder the hunger I feel during my period has reached a whole new level, I eat, my body thinks 'Great, finally famine is over' and I can easily eat 4-5k calories in a day.
Your body is not just doing this because of hormones, it's doing it because your overall diet is too restrictive and it's taking the opportunity to nourish itself when yout hunger spikes during your period, my friends and family are actually shocked by how much I can eat when I have my period or I am feeling brave and allow myself more food but I'm not, that's exactly what happens when you don't eat enough for the majority of the time and although it scares me I just go with it now, I am certainly not 'fat' either, my BMI hasn't been above 19.6 all year and the last time I checked it was 18.9 so clearly my body needs the extra food.
1500 calories is a diet amount anyway, you are only 16, probably more active than you think and need around 2000 on an average day, I am 41, 5ft 1 and lightly active and I can eat 1800 and not gain weight, frankly I'm too scared to do it but I've been in recovery enough times to know how the human body works and trust me you have nothing to worry about apart from the fact that you just don't eat enough on a day to day basis.