Yeah, I think that is pretty common and yes I did the same thing.
I sent CQ, someone answered me, I went into a blind panic and shut off the radio.
Of course now I can't understand why I did that. But, I was a teenager at the time and that was a long time ago. It was in 1979.
I guess it might have been the long anticipation of that moment that did it. I wanted to be a ham since I was a little kid. Finally as a high school kid I found an Elmer, studied the code for about two weeks, passed the code exam. He sent in my application and received the Novice class theory test back in the mail. I took it. We sent it in to be graded. Weeks later my license arrived. Like you said, the process might have took months.
And finally when the whole thing came together I was overwhelmed.
FWIW: I was using a Ten Tec Century 21 with a straight key into a random length end fed wire. I was using a tuner that I homebrewed on a piece of wood. I wound the coil on a plastic shampoo bottle using a stick from a kite to hold the turns up off the bottle so I could tap the coil. Along with a cap out of an old broadcast receiver. And a Radio Shack SWR bridge. Was putting out about 30 watts.