I tried to take some pictures of a Mr. Ben Cave using only candle light yesterday and in camera most of the pictures looked great. No issues with color, sure they were a little orange, but hey, it's candlelight. Upon loading those pictures into the computer I was met with pictures that seemed far under the quality of the in-camera pictures in which most of the colors were running together and ultra oversaturating, losing massive amounts of detail and horrible color inaccuracy. Here is one example:

Upon further inspection I found that many of my pictures were doing this to varying degrees. Like this one (the color distortion is mainly in my forehead):

How can I fix this problem? Do I need to shoot in Raw or a different setting? Is it my monitor? I'm stumped, so any help would be great.
EDIT:
If I turn off the high saturation in camera and pump it back up in computer then it seems to rectify the situation. But this seems like it would be a horrible chore to do to every picture that I take in the future. Tips?