I have just e-filed my taxes last night. Today I received a 1099-INT from my bank. What do I do now?

It depends.  Technically, you need to prepare an amended return.  Your tax result may change slightly with the addition of the interest.  And if it does you should pay back the difference (it should be minimal) to avoid any interest or penalties.  However, if you prepare the amended return and it shows no difference in tax due, then you will not need to file it.

Right now, you will not be able to amend because the return must first be accepted and then the refund issued.  Probably around mid-February, we will have instructions on how you can prepare your amended return this year.

One other possibility is if your e-file is rejected.  If that happens, then in the process of fixing the return for e-filing, you may also add the interest amount as well.