How to amend my tax return after receiving spouse's ITIN?

In 2017, I was a tax resident of the USA, while my wife was a nonresident alien. She did not have any tax number at that time yet.

When the time came to file our taxes in 2018, I checked the "married filing jointly" box, left the spouse's SSN field blank, and attached a W-7 form to the tax return, so as to apply for her ITIN simultaneously with the tax return.

The ITIN application was initially rejected, because of (supposedly) insufficient documentation. Consequently, my tax return was processed, but without taking my spouse into account. A refund was deposited into my account, but the amount was smaller than what I was expecting.

We then reapplied for my spouse's ITIN. If I remember correctly, I included a copy of the original tax return in the envelope, but I am not 100% sure about this. Recently, we finally received the ITIN.

Now what should we do in order to receive the missing amount of our refund? Can we simply expect the IRS to send it to us without any further action? Or should we send an amended return (1040-X)? If so, how should we fill it?