To elaborate a bit, boys get hard unintentionally all the time, especially boys your age. Males usually get hard several times a night, but one of those erections almost inevitably happens somewhere around the time we wake up. That is morning wood.
On the other hand, wet dreams are spontaneous ejaculations - they may or may not come with a sexy dream, but they are characterized primarily by making a mess in out pants (if wearing any) and/or sheets. Also, they happen rather rarely, mostly when the male has not ejaculated in other ways for a few weeks, so it mostly afflicts younger boys or boys wearing chastity devices, and maybe some males who abstain from sexual stimulation in more conventional means. Often those happen closer to the middle of the night, though I guess it would not be impossible if one happened in the morning. However, they are much more rare than morning wood, so no, wet dreams are most definitely not the cause of morning wood.
Heck, it is not even particularly sexy dreams that cause morning wood, or horniness. Might actually be the other way around, that morning wood causes horniness since when the penis stands at attention, that might be enough to put many guys in the mood already. It is simply a physiological matter. Muscles relax, blood vessels dilate, and that causes blood to rush into the penis.
