Software for making a 3D globe out of an image

[Midgardsormr]

Create a flattened layer with your map. Then in the menu, chose 3D > New Mesh from Layer > Mesh Preset > Sphere.

Photoshop will create a 3D sphere and wrap your map around it. Note that you'll need to have an equirectangular projection in order for this to work, since the texture will be pinched at the poles.

I'm not terribly familiar with Photoshop's 3d features, so that's pretty much the extent of the guidance I can give you there, but I encourage you to play around with it and see what you can do.

edit: These instructions were formulated based on PS CS6. The 3d feature set was introduced in CS4, so I know you should have access to it, but the exact procedure may be different.