You are probably not looking at an "editing" program, you are looking for a "composite program". (An editing program is to assemble video sequences one after another. A compositing program is to assemble elements inside sequences one on top another)
Frame by frame... probably any compositing program can do that but that is too primitive. Now you can use tracking motion.
Take a look at HitFilm Express, that is free, and has 3D tracking. You can inclusive select a pimples on a person's face, and the program tracks it on a series of frames, and you can put something over there.
You can use Blender, that also has motion tracking. Also free.
After Effects is a compositing program too but this costs some bucks. You can use a monthly subscription. (But you can do that in HitFilm for free)
If you require a more advanced frame by frame retouching use Photoshop itself.
Photo Paint also can edit video.
And Gimp with a plugin GAP
The problem with this last 3 is that you are not editing a "video" but a ton of layers, one per frame, so you need to keep your sequences short.