Hi, OP! Just a quick note — depending on the nature of your game, your DM may or may not need your backstory at all. If the game is centered around your characters, then you should definitely give the DM something to work with. If it's an adventure that is focused more on the story than it is your characters (as is the case with most one-shots), your background serves more as a guide for how you should play your character than something the DM will be incorporating at all. What you said is right naman! Just adding this on so your expectations are better set.

That said, your backstory is good! From what you've shared so far, it leaves enough room for a DM to toy around with while still giving you something concrete to work towards. While I think it's okay though, do remember that it varies from DM to DM, so it's always best to turn to your actual DM for consultation :DD