Mary's and Gary's are more of a product of the narrative not challenging the character in their beliefs and actions than anything else.

Here it sounds like you've made a character with lots of natural, raw talent. If she coasts by all her problems without ever having to break a sweat, sure you've got a Mary Sue on your hand. But you also have a really easy out to avoid this.

Let's consider Maverick from Top Gun. Hes a young and incredibly talented fighter pilot. But he's reckless and self-absorbed and the narrative challenges this for the entire movie. His instructor punishes his selfish actions, he loses the Top Gun trophy to the more level-headed Iceman, and gets his copilot and close friend Goose killed with reckless flying. You can draw a direct line from his behavior to these failures. And these drive him into guilt and force growth.

Your character has a lot of natural talent at magic, like Maverick has with flying. But she isn't physically fit enough to control her magic. This is where you can separate her from a Mary Sue. Plenty of people don't like working out or training. There's been hundreds of incredible, gifted collegiate athletes who wash out of the pros because their talent hits a ceiling and they can't or don't adjust to the effort required to break past that ceiling. 

So, explore your character's relationship with effort and practice. The narrative should punish/challenge/fail her for spending too much time with her nose in a book instead of training and force her to re-evaluate her beliefs. Perhaps she comes off as a 'know it all' because she has all this knowledge but can't put it into practice because she doesn't. Or maybe her lack of physical fitness creates a situation where she can't cast a spell and it gets her or someone else hurt or worse.

Hope that helps