Get a cup.
Seriously it helps. I used to be like that, even had a phase where I didn't go to sleep at all during the first day of my period. Looked like Dracula's daughter the next day, because of the rings under my eyes. :D
Since I'm using the cup instead of le ol' tampon I'm sleeping like a rock (as I always do). It also helps with the anxiety of leaking during the day. ;) I don't even think about my period anymore, well... aside from the occasional “did someone just push a knife through my uterus?“-feeling.
You just have to find the right one for you, considering they're dependent on the position of your cervix (high/low) and whether your pelvic muscles are strong/weak and in the beginning it can be tricky to get it in. I suggest trying to put it in while not being on your period (just to prevent reenacting a scene from Texas Chainsaw Massacre).
Plus: It's saving you a shit-ton of money and it's eco-friendly, due to being reusable. :)