I would like to start narrating the clip I'm editing, freezing the video but continue narrating for a while, then continue the video.
Is this possible at all in Premiere Elements? Or do I need Premiere, or another video editing software?
This is possible in PrE. The exact workflow might depend on what you have.
One example would be if you knew exactly how long you want the Narration to go for, and hence how long the Freeze Frame was going to be, you could just do a still from the last frame of your Clip, drag it to the Timeline, and drag its Tail to get you the Duration that you need. Then, just do the narration, on any empty Audio Track. The Narration Track usually is good for this, but some users have encountered problems with it, so do not hesitate to choose any free Audio Track.
Another workflow would be to record the Narration. If you need to position the beginning, address that now, and also any editing, say removal of dead air at the beginning, until you are satisfied. Then basically use the steps above, but make sure that any addition of the Freeze Frame does not affect that narration. When editing, you can use the Ctrl key modifier as is needed.
Basically, you are creating a variation on an L-Cut, but instead of motion in the Video, you are using the Freeze Frame, and using the narration, rather than the Audio from the Clip. For more discussion on J & L-Cuts, this ARTICLE might be useful.
I like doing my video editing first, and then adding any Audio, whether narration, music or SFX, as my last step.
Good luck, and welcome to the forum.