Disable leaf bones in the export.
Check the apply all modifiers on the main tab.
Change smoothing to faces only (to see if you get any differences).
Export only a base pose in A or T pose to get a master skeleton going with the proper mesh.
import in unreal - I would reset all the settings just to be sure first. Disable the animation when taking in just the master pose.
this will create the mesh, the skeleton, and optionally the materials.
Secondly, export the “raising arms” animation without the mesh.
select only the armature in blender, export the FBX
Check the only selected box during export and tweak the values as above.
When you import into ue4 now, you will just be taking in the bones.
Select the previous skeletal mesh during import.
Play the animation and check to see if you are still seeing the issue.
hopefully you won’t.
If you still see the issue I would suggest getting rid of the shape keys first in the master pose, import in a fresh one after deleting the skeleton/mesh, and repeating the steps.
try and isolate if the issue stems from the mesh or from the shape key associated with the mesh.
afterall one of your edge loops is bulging out. Something is causing this, and it can’t be the bone rotation or everyone would be complaining about issues.
Oh and within blender - what type of bones are you actually using?
normally you would use the octahedral or whatever the ones that look like cones are.
you can change the display to sticks, like you seem to be doing, but you could also be using bendy bones, which aren’t going to work in UE4.