So I want to animate from the segment you can see in the first picture to it being slightly morphed like in the second picture. I can’t keyframe in edit mode it seems. I’ve tried keyframing it in object mode in the first picture at frame 0, changing to edit mode, moving the vertex to match the second picture, then going back to object mode at frame 10 and inserting a new keyframe. Unfortunately this does not work 
any suggestions? 
What does “not work” mean in this case?
What keyframes did you use? LocRotScale would probably be needed.
You can’t directly animate edit mode changes.
What you can do is create the second shape as a shapekey of the first, and animate the strength of that shapekey.
actually you could do it with this addon -
you’ll may have to re-name it though for some reason in order to install it, at least I had to on linux.