MJ,
Instead of carefully creating two (presumably only almost) identical halves, then delete one, and edit the other half without seeing the whole shape while you are at it, and then reflect a copy to see whether it is satisfactory, maybe having to go back (and forth), you can work with the whole shape in one go.
Illy (job description Adobe Illustrator, she is always very helpful) can help you do it in one go and see it while you are at it in a few ways.
Smart Guides being your friends, one safe way is to:
1) Create a rectangle larger than one of the halves, thenCtrl/Cmd+C+F (hold Ctrl/Cmd and press C followed by F) to create a copy on top, then deselect and ShiftClickDrag by one of the far corners to snap so you have the two rectangles with one coinciding side;
2) Select both rectangles and Group them, then Effect>Distort&Transform>Transfor>Reflect with 1 copy, then lock both rectangles within the Group;
Now you have a frame to work within (you can set a copy aside to reuse for other mirroring tasks);
You can set the stroke to none to work undisturbed by them, relying on Smart Guides.
3) With the Pen Tool, ClickDrag (or just Click) on a suitable spot on the centre line, then drag the new path into the Group, and simply draw one half as an actual shape; as soon as you have the second Anchor Point you can (begin to see) the mirrored shape; you can use Ctrl/Cmd+Z to undo and then redo parts, and when finished you can switch to the Direct Selection Tool and adjust the actual shape and see the whole shape straight away;
4) Delete the rectangles when you are sure, then Shift+Ctrl/Cmd+G to Ungroup.
You can keep the heart (or whatever) as an effect or Object>Expand Appearance and join to have a full actual shape.
For multiple reflexion/rotation axes and plugins, you may have a look at solutions in this thread, including the links to external solutions below:
https://forums.adobe.com/thread/2284752
Or you can have a look at the MadPattern templates,
http://madpattern.com/
Or you can use the MirrorMe plugin from Astute Graphics,
http://www.astutegraphics.com/software/mirrorme/