First,

The 1937 proof Buffs are all brilliant proofs with smooth, mirror-like fields. Several distinctions exist between the proofs and business strikes. First, the feather tie is much more distinct on the proofs. Second, the rachis is plainly visible in the first feather. Third, the detail on the buffalo's belly, eye, and leg sinews is much sharper than any business strike. Fourth, I've never seen any die clashes or clash polishing on the proofs.
The proofs also have distinctive die polishing marks. On the obverse, one die pair has sharp SW-NE polishing marks on the curve of the Indian's neck, and the other die pair has weak horizontal polishing marks in the first feather. On the reverse, the first die pair has E-W polishing marks in the curve of the buffalo's neck directly below the "U" of UNITED and N-S polishing marks from the buffalo's belly to the ground level. The second die pair has SW-NE polishing marks through the upper horn and slight pitting above the buffalo's head.
Your coin is a business strike, but early die state. It has the tell-tale golden toning of an old album coin, almost certainly an old Wayte Raymond / National Coin Album, It's a beautiful coin.