No. If your spouse prepared a joint return correctly and included all of the information and income from both of you on that joint return, then you are done. You do not file another return of your own. The joint return was for the two of you. The refund will come in both of your names. (or you will jointly owe the tax due).
Do make sure that your spouse entered your W-2's and/or 1099's on the joint return. Sometimes newlyweds filing first joint returns get confused and do this incorrectly.