Here's what I do when working on a fairing or something...
Using point select I'll highlight the bulk of the points south (or north, whatevs) of the "equator", but not those located on the "equator" (I'm using the word equator as a substitute for the horizontal line, but I guess you could probably figure that out...).
Anyway, once selected, delete them. Now zoom in and enlarge the nose section to take up as much real estate as you can. And use the machete that N_Molson referenced to make one (1) small cut at the very tip of the mesh as close to the horizontal split as you can make it. If you don't do this, you may wind up with a very small hole in the fairing that you'll not notice until much later.
Anyway, making this cut will create a new point. Do not delete this point, but delete all the other ones on that side of the mesh. You should be left with only half a fairing, mirror this along the horizontal axis and you have your fairing.
There are other methods, but this one is pretty quick and cheap.