When you shoot in jpeg, your photo is corrected in camera to account for barrel distortion as well as contrast, color saturation etc. You will therefore find that straight out of the camera your jpeg files will generally look much better than their RAW counterparts.
RAW files keep all of your camera's original data giving your more control while editing photos and the ability to pull information out of the photo that a jpeg file may no longer contain. If you just want to be able to throw some great pictures on facebook, jpeg may be all you need.
Programs like Lightroom (highly recommended) have lens correction profiles for many lenses (including your 16-50mm) which, when enabled, automatically correct for barrel distortion, chromatic aberration etc.
Barrel distortion is not limited to zoom lenses. The 16-50mm lens you have is a fine lens, and it's size and weight make it ideal for backpacking. There are much better lenses out there of course, but none (that I know of) have similar size and weight that cover such a useful range as the 16-50mm.
If you do decide to get another lens, my recommendation is to use the heck out of your 16-50mm and see what focal length you typically take pictures and what situations does the lens limit you. For me, I found that I shot at 16mm much of the time, but each photographer is different