If you don't see that EDIT option, I'd recommend performing clean reinstall of your Spotify mobile app. It's different than regular reinstallation. Just find your device in this article and follow the steps provided there.
If you can't change your personal information on your account overview, it's most likely because you created your Spotify account with Facebook.
In this case it won't be possible for you to change the email address on your own, but you can reach out to Customer Support and they will be happy to update it for you.