1951 Wheat Penny Possible Error

Based on the amount of wear, I doubt so.

Thank you

You have a circulated business strike Wheat cent. In BU condition they would look something like this:

Click to enlarge image
A proof coin would look something like this:

Click to enlarge image.
Note the differences in the finish of the coin.

U.S. Business strike cents are used for normal circulation.
A proof coin is special created for collectors in mind. They are not better strikes of the regular coins, the are specially struck. When circulated these coins will still be called a proof coin with a lower grade and called an impaired proof.