How to cut a model so that it can become like a easter egg capsule?

Hi, I am learning to cut and use the knife with Blender but cannot get anything to work at all. I am trying to take an egg shaped object and cut it so that there is mating overlay in the wall thickness to create the Easter egg where when I 3D print it I can snap them together and place something inside it. How can I cut the object but make the 90 degree turn in the cut within the wall thickness and then rotate this cut along the perimeter of the object? If it makes it any easier, I can make the outside of the object a single mesh and then solidify inversely to create uniform wall thickness.

Try the bisect tool

Start from a Circle, design your interlocking part. Then create egg shaped object, snap in your interlock.

Ok, I already have the object that is egg shaped, how can I get these interlocking ridges in it?

Also, how can you snap in a interlock? Blender is so different than solidworks.

Blender ain’t a CAD. It’s a polygon modeling software; you approximate things, so, yes, it’s different. Like a vector drawing app and paint program.
Select and delete or V- rip edge loop where you want egg to come apart. Separate top/bottom meshes - select one part (L-key) and P to separate. Take care to have same amount of vertices on a rings for interlock and egg.
Use Snap to Vertices and, well, snap parts. I doubt i could explain this in detail, will take a wall of text; better see if wiki or youtube has something.
Last, select 2 rings of vertices and W - Bridge Edge Loops. Repeat for both top and bottom, inside and outside shells.

Since you are likely just starting to mess with Blender, easiest would be to get familiar with how proportional editing works, take interlock mesh, extrude rings from there Z, Ctrl-r drop in some edge loops and scale upper (lower) ring while you get egg shape you like.