In my view, the nickname is usually introduced through dialogue or some kind of interaction with an outside source. A person usually does not call themselves both a formal name and a nickname, so it wouldn't be something to put in a description. You would introduce the nickname spoken from a different character, such as "Kayley turned around and saw her friend waving frantically in the air. 'Kels, you've got to come see this!' the other girl shouted."
It's the opposite if a character calls themselves a nickname instead of a formal name, like if they don't like their formal name. In that case, the nickname would be how you address the character and the formal name would be used in dialogue.
An exception would be if the book was first person. In that case, you could write...
formal --> nickname
"Well, I'm just a southern girl named Belle, known to my peers as Southern Belle."
nickname --> formal
"My name's Dan, NOT Danielle as my mother refers to me."
It would just be awkward if you switched from a formal name to nick name in the middle of description. People don't refer to themselves constantly by different names. They choose either the nickname or the formal name and use that as their description.
As for your specific question...if you started out describing them by a nickname, and didn't change in the middle of description, it should be fine. It's just weird when it keeps going back and forth.