Is there something wrong with my camera?

This is an unedited photo I took of my niece. It was shot at night indoors under mixed lighting. Tungsten and Fluorescent. I've been messing around in photoshop, but I can't seem to get rid of the red cast and it's making me wonder if there is a possibility that there is something wrong my camera itself.

 

But when I used my on camera flash it seemed to be okay. Maybe I'm worrying over nothing?

I didn't do ANY editing to these photos. After looking at the difference between the photos where I used my flash, or didn't. I've come to the conclusion... I worried over nothing. :HUGE sigh of relief:

What irks me is that some of my best shots were done without the flash and they have a horrible color cast to them that I can't do anything about. GRRRRR