The first problem with your pics is you are using a pop-up flash. If you're going to use a DSLR, pop-up flash, and auto settings you could have saved several hundred and just got a Point & Shoot to get the exact same image.

With that said, if you took a Canon Speedlite 430 and pointed it toward a 8'-10' ceiling or sideways to a wall and put it on "Portrait" setting you could produce a shot that looks magazine quality compared to the pop-up flash. You could also try using a white envelope or anything reflective to bounce the light from the pop-up flash off the ceiling - it will produce a completely different image.

Second problem is the images aren't distorted, they're blurry from being such a low aperture and slow shutter. When the settings are on Auto it will sometimes reduce the shutter to a speed that can't possibly produce crisp images [in order to expose the image properly]. There's nothing wrong however with shooting in Portrait mode when bouncing an on-camera flash (Speedlite) but your best bet is to invest in a strobe, or two, and learn manual settings.

I challenge you to take a shot using the pop-up flash direct then using an envelope reflect the light towards the ceiling and post up both shots. This won't be nearly as effective as a Canon Speedlite pointed toward the ceiling but still far better than direct light...