SarahSalt is right, the larvae are what are eating your clothes. They prefer clothes that are not 100% clean. Clean everything-especially wool and furs-moth larvae are attracted to dirty (previously worn) clothing. Take everything out of the closet and vacuum or wash the floor.
If you have pets, make sure they don’t get in the closet and you don’t store their items along with your clothes. I couldn’t figure out where moths were coming from in an apartment I had, then I realized they ate fur. My furred pet liked to sit under the middle of my bed and clean himself. Bingo-food source located and cleaned up. Killing the adults and any larvae after that took care of the rest of the problem.
I don’t know if lavender sachets work, but I keep them in my drawers just in case. When I store clothes in boxes I clean them first and then use cedar balls. You can get them cheap at Target. Don’t let pets chew cedar items.