Some might say, Richard, you're trying to hard. You're not even through a third of the chapters of Psalms with your questioning if "Jesus could pray this Psalm" and you're having to dig deep to make ot fit. Even though it was the Holy Spirit who inspired men to write the Scriptures we read, it was men and women who wrote with their own heart and feeling. These writers, very evident in these psalms, wrote from the depth of their humanity. Since Jesus was fully man and fully God did He or did He not face the possibly of the same depths of the human spirit?.
To the excellent musician Jeduthun
I thought, I will take heed to my ways, that I sin not with my tongue: I will keep my mouth bridled, while the wicked is in my sight. I was dumb and spake nothing: I kept silence even from good, and my sorrow was more stirred.
Psalms 39:1 - 2 GNV
Long ago I was helping with a bus ministry to unchurched families. As the children got older, 12 or 13 years old some parents no longer told their children or even grandchildren to go to church, but some kids asked if they could go to a friend's house or just play in the neighborhood instead. Often they would choose to go with the friend instead. As I considered this I thought that most kids in church may probably choose to go with friends instead. The challenges of choices of young people at that age.
As I read in Psalm 39 I wondered how Jesus thought about things as a teen or preteen? In other words did Jesus possibly think something like this psalm before OR after He spent three days in the temple asking and answering questions? The feast was eight days. Did He feel like He had to wait until the end of the days of Unleavened bread before He could speak in the temple? Did it burn in His heart as a young man to be able to speak? At twelve He knew what His Father's business was to be doing, but the timing wasn't the right time to do it. In fact the right time for that was apparently another eighteen years.
While this psalm sounds like someone trying to hard, first not to speak, and then his heart burned to speak, it represents a struggle to know when to speak, what to say when speaking, and the right way to say what needs to be said. No, this psalm wasn't the type that Jesus might pray, but it certainly poses reason to think about and consider what we know of the typical nature of man through the different stages of growing into becoming that man and how that might apply to the life of Jesus. The nature of that growth was very different in the days of Jesus both in culture and mindset. Even so emotional changes are a part of growing up no matter when and where.