Here is how the IRS works.  They are going to get a copy of the 1099-B.  Generally, the IRS looks at the gross income and generates a CP2000 (income matching letter), billing you for taxes on the gross amount as a short-term sale.  This is a computer-generated letter (that's what CP means).  It will come, but it could take months or years.

You can amend the return now, or wait until you get the letter and respond to it then.  I would wait until after the tax season rush is over, to see if there are any other changes needing to be made, and then send the amendment.