You can try using an app like Photosynth, which creates stitched images from a set of images by seeking common features. Unlike some apps that only stitch panorama left to right, this allows for both up-down and left-right, which makes it a good choice for your purpose.
Using the latest in computer vision techniques, you can not only make a panorama from left to right, but also up and down, enabling you to capture a full “sphere”.