This is how sword plants reoproduce. It will eventually be a baby plant. You are obviously doing things right or it wouldn't be reproducing. Let the baby plant stay on the shot till it is about 3 to 4 inches tall and you can clip it and replant it.
So, the vertical shoots are the plant's effort to get a flower growing above the water, for sexual reproduction. Failing that, it just switches gears and reproduces without benefit of a partner? That is what appeared to be happening, but none of those vertical shoots ever made it all the way out of the water for me as best I remember.If it makes it out of the water, it will flower and may produce emersed small plants. If it stays submerged, small submersed plantlets will result.