Copyright for artworks in this context is automatic. At least that's how it works in the UK. Once your create your own art, you hold the automatic copyright. Unless you made the art under commission to someone else.
Now I might be wrong but that's the impression I have had for years.
You are granted copyright automatically yes, and this gives you certain protections like the ability to file DMCA takedown notices etc. However, in order to sue for statutory damages you have to have filed the copyright with the US Patent and Trademark office before the infringement occurred. You can still sue if you register after, but only for actual damages which is harder to prove.
Not entirely true. Under 17 USC § 411, if you are bringing civil action against someone for copyright infringement, you must have registered your work. However, under 17 USC § 106, owners of copyright have exclusive rights to their works (with some caveats), which doesn't have any baring on their ability to sue someone for copyright infringement.
Where I'm a little hazy is in my reading of 17 USC § 411(c) - I believe that you can only sue for copyright infringement within 3 months of the work being "first transmitted" (which I assume also includes publication), and 48 hours after the work has been "transmitted".
Now I might be wrong but that's the impression I have had for years.