Why would you not? Of course. Personal experiences make for some of the most moving, funny, interesting and fascinating stories. We have the most to write about experiences that are real.
Does your grandma not want you to write about the experience? Are you afraid she might see it and be offended? Sometimes it's nice to just write about things that you want to write about, and keep them just for yourself - most of what I write will never be seen by any other person.