No, simply because a prison is for those awaiting trial or who have been sentenced. Not everyone on earth falls into these categories. If you mean are we prisoners because we’re trapped on earth, well the answer is no there too because some people have been in space. So as a people no, individually, technically no, but we all know I’m not getting a ride to the moon anytime soon and neither are you probably.
Something to consider, and I remind my self often that the only true prison is your mind and the bars it closes you in.