I think you did a great job. Comparing a heart to a bird flapping in a cage gets your point across, followed by some accurate-seeming description. I don't see an issue with it (but I'm not too experienced).
You used a simile (the bird flapping) to describe the feeling. One idea could be to form it into a metaphor. That is less literal and brings the reader into the mind of the character more, and figurative language can oftentimes show emotion better. Maybe "A panicked, caged bird was flapping inside of me. I heard the thumping. Maybe it was my heart, for all I know."
When you ask the reader if they've ever seen a wild bird in a cage, that makes it seem more like a conversation, like the character is casually looking back on their past experience. Like your story is a building that you're looking at from a hot air balloon. If that's the goal then you nailed it. "You" is 2nd person. But if you want it to be super urgent and in-the-moment, like you're inside the building or right on top of it, pausing to ask the audience a question might pull someone out of the moment. If I'm not making sense, I'm sorry for being confusing. Overall it's good. Keep the bird.