No, you cannot file a separate form 8889. You will have to amend your original return to add the 8889.
Since you had contributions to the HSA, the IRS requires you to complete and attach a form 8889 to your return. If you don't include it, the IRS assumes that all your contributions and distributions are taxable.
This will cause the IRS to send you a letter asking for the completed 8889 or for an amended return with the 8889 or for just the tax with possible penalties and interest.
If you entered a deduction on line 25 on the 1040 for your HSA contributions, you can expect a letter pretty quickly asking you for the 8889.
However, if you made no such entry on line 25, it will take the IRS longer to compare your W-2 and other data and realize that you should have filed the 8889 with your return. In this case, their letter may include a request for taxes, penalties, and interest.
Filing your amended return quickly will help cut that off.
Next year, please use tax software that supports the 8889, and file everything all at once.
