I told my gf i needed space since I've been extremely busy with school and taking care of my grandma. She got upset, cried for 2 hours, told me how I've mistreated her. And accused me of cheating/ when I didn't and told everyone. Am I a douche?
You're not a douche.
But I know what it feels like to be an insecure woman. Maybe reassure her that you care for her, but truly need some space for the reasons you listed.