By creating something depending on your jurisdiction you're protected by common law copyright.
I am not a lawyer but if you search online you'll find info on this, you can but no there is no need to submit to any institution, copyrights are automatic:
https://guides.dml.georgetown.edu/copyright/creators
https://medium.com/rightsledger/copyright-basics-for-content-creators-968ade8a4c...
edit: this is in the US not sure about other places