I have been added to an organization that has some private repositories and I need to send them a pull request with some changes but I don\'t know if I can.
As mentioned in "If I fork someone else's private Github repo into my account, is it going to appear in my account as a public repo?", you can fork a private repo (for which you were added as a private user). The resulting repo will still be private, and you will be able to make pull-requests.