Something like 3/4 girls and 3/5 is sexually abused in this country. It is hard when it happens in your own family. Of course you're going to feel many many things like anger and depression, even hopelessness. Was the rapist in the family, or not related? I'm sure the child's parents (if they're not the abusers) need a lot of support too. You'll get through this, but it's going to be rough. If your little cousin gets good therapy, they'll learn how to manage.
Man, it sucks, though. I'm so sorry this has happened in your family.