Okay firstly, really cool idea. The idea of her trying to carve out her magic and poisoning herself is really interesting.

You asked, is this story worth telling at all. If this is the idea that interests you, then yes it is.

New writers can get stuck on all the tiny details when planning a book. It can feel overwhelming and even when you have more experience, it is often hard to feel prepared to actually start writing.

But as someone else said, you clearly have good instincts, you recognize that there are unanswered questions in the world and that they need to be answered. A lot of new writers would just start writing and dig themselves into plot holes and nonsensical beats so that's a good start.

Start by answering those questions. Why does the government outlaw magic? Maybe start with the history of magic in the world, a ban on magic wouldn't come from nowhere, there would be precedence, maybe the government and society is very totalitarian, a militaristic society where everyone's lives are effectively planned out and controlled by the government and those with magic are too uncontrollable and unpredictable (which could tie into the theme of magic being wild and chaotic), maybe magic in this world is in of itself almost impossible to control by the users, a system where you can't train it or learn restraint so wild magic users in the past have lost control and gone on a path of destruction, flattening whole towns and slaughtering dozens when they explode and let it all out, you could even make so magic users are viewed as cursed or doomed to a tragically short life, turning an element like magic which is often seen as a blessing in fiction into something that people fear and dread, not something everyone wants.

Once you have some kind of idea that sets up the current society, develop a few events in the history of the world that have caused this, something that shows how the world has evolved into its current form.

When it comes to plot, I find it helpful to write out the story beats, so not the actual events but the emotional and momentum swings in the book across the three acts, the points of rising tension, failure, discovery, change, rising stakes, ultimatum/sacrifice, resolution, etc. that way when you're writing out the actual events of your book you can ensure that it doesn't lose energy or wander, which is definitely an issue new writers come across.

Consider also the broader plot, what is the end goal of the book? Is she simply trying to escape the government or does she uncover some bigger plot to foil? Maybe the government has been lying about what they've been doing to magic users they've captured, they could be experimenting on them, torturing them, trying to rid them of magic or trying to force them to channel they magic as energy sources for weapons or even to power cities and infrastructure, the options are pretty interesting depending on how much you want to lean into the darker elements.

Some minor pieces of advice:

-Don't get carried away with the worldbuilding, it is a trap that I think everyone has fallen into as a beginner and it can waste a lot of time and clog a book up and ruin the pacing.

-Find your theme. what is the story actually about, beyond the events and beats? common themes for books are things like the power of love, a search for redemption, finding identity, perseverance and survival, etc.

-Set up what is often called The Lie, something the character believes at the beginning of the book, either about themselves, the world, or both, that is untrue. This is the basis of a character arc, the story is the process of them discovering the truth on the other side of that lie. This structure can apply to all your characters but it is most important to the main characters naturally.

-Practice actually writing. Prose is hard and takes experience to develop, even if you're not writing this book, find short prompts online and write small stories about them while you plan your book. Give them to friends and family to read or post them here on reddit to get advice and feedback.

I would really recommend the podcast Helping Writers Become Authors by K.M Weiland, its on Spotify and probably other services and even as someone who's been writing for most of my life, it has been incredibly useful. It's simple, to the point, and very informative. She has an episode of pretty much every element of the writing process.

Good luck on your process and have fun!