Can I be obsessed with death?
Why are you obsessed with death?
Being obsessed with death is a part of mortality, death is a part of life.
While death does happen to everybody  and it is a natural part of life, it is not good to obsess with it so much. It can stop you from living your life.
It's an endless circle and it's temporary. I'd rather embrace it than be afraid of it.
Again, you can embrace death, but focusing inordinate amounts of energy upon it is counterproductive. Focus your energies on lots of topics instead of just death.