Yes, you are required to amend your return to file an correct and accurate income tax return. Your cost basis should be the same, your cost basis, whether you file a return or don't file a return and does not change.
You are required to include all income on your US return if you are a resident/citizen of the U.S. if meet the requirements to be required to file a return.
If you file a return, even if you are not required to file a return, then you must include all income on it. You cannot pick and choose what income to include.e.
