If someone were to claim the work as their own, their only option would be to file a DMCA notice against you and have the video taken down.
If that were to happen, you would easily be able to file a counter to it, claim the video as your own, and their only recourse would be to take you to court.
If they were to steal your video, upload it as their own, and then try to claim against yours, YouTube would simply have to look at the upload dates to know who came first.
A more likely scenario is that your video gets wrongly claimed under Content ID, an automated process that searches uploads for known music or video, but, again, so long as you have all of the proper rights to use everything or are able to prove you made it yourself, that’s easily countered as well.
If you’re that worried, I’d recommend adding a watermark somewhere on your video. That way it would be obviously your and, if they try to claim it as their own or repost it, they’d have to crop or modify it in some way.