Does a ceiling header work as a window/door header?

We are turning a 3 season porch into a 4 season. We are starting to frame in the doors and windows. We threw this together for the picture to and will try to send it to the local inspector this week to see if it sufficient (thought maybe I could get a quicker answer here). With the doubled up 2 x 6 only 5.5" from the top of the window, we weren't sure if it was necessary for another double 2x4 header? This opening is for a 48 x 48 sliding window. Thanks for your help!