I like this story. The ending is strong, and the description of the girl/owl transformation is clear and effective. The boy’s problem with dad vs. vocation is clear.
A few things to consider:
It needs a title.
While the situation is presented, there isn’t much of a hook. See if there’s a way to raise questions from the very beginning and not just set things up. Magic, his father’s power over him, and his delight in drawing all provide good elements to explore.
Charley meets his opportunity with disbelief and no action until the very end. Did he learn anything? Did he find something that propelled him into action?
He did get some information, which might have been provided by a teacher rather than a magical creature. Did he go from not being able to run away to being able to by the end? If so, what created that growth?
In general, the second part of a story (in this case, the meeting with the owl/girl) will have escalating challenges and rising stakes. Here, Charley is fairly passive with repeatedly disbelieving. In general, repeating is not your friend. It makes the story plateau. (In fables, there can be sets of three, but usually, they all are subtly different in what happens or context. Occasionally, the repeat may be an incantation if it’s poetic enough.)
The bones of this one are excellent and promise a wonderful story. Nicely done.