On the conditions that the language is general use (i.e., doesn't perform the task in 1 character) and follows the rule of having been invented before the question was asked. I've written languages before that were inadvertently good for code golfing, and I wasn't sure if those would be allowed as valid solutions.
Yes, this is fine. A quick look around the site will show an abundance of answers in languages created by PPCG users, and used nowhere else. The one thing to avoid is modifying your language in order to better solve a specific question, and then answering that question using the new version. Thus, it is preferred to answer a challenge using versions of your language published beforehand.