Weight loss?!

I got the nexplanon implant when my daughter was 6 weeks old, and since then I have gotten the biggest I have ever been... I feel huge! It has made my weight gain insane, my depression super bad, and I'm losing handfuls of hair all day every day. I am scheduled to get it out next week, but my question is how do I lose the weight without affecting my breastmilk supply?! If I am supposed to eat extra carbs and calories for milk supply, how will I lose anything? Especially since I've read stuff about exercise making some mom's supplies tank? Anyone know what to do?