Welcome to Coin Community, Matt. Ratman has the "Open/Closed 3" thing right; on this coin, the "closed" version actually touches so at first glance it looks like an 8 instead of a 3. If it looks like a normal 3, then it's Open. The Closed ones are rather easy to tell. They're a real rarity, only 1800 having been struck of the 125,000 total mintage.
As to whether or not it's a Proof, well, if you paid less than $15,000 for it, it's not a Proof.
Only 25 were minted, fewer than that exist today, and it's one of the true rarities of U.S. coinage. If your coin is an Open 3, that will be conclusive; all Proofs are Closed 3's.
As to whether or not it's a Proof, well, if you paid less than $15,000 for it, it's not a Proof.





















