This is a relatively common failure with the C7. Unfortunately, it is also fairly labour intensive as the front nose / bumper cover has to be removed in order to access the headlight modules.
I can't recommend a servicing agent as I would do this replacement myself, but I will offer a few suggestions.
First off, replace both bulbs. If one is gone it's just good insurance to replace the other. Any quality, name brand bulb will do the job but pick one with a good, realistic replacement warranty. If, by chance, the bulb replacements don't solve the problem then it's most likely that the ballast has failed. If this is the case, I would replace only the defective one.
As for the 6000K colour selection, this is very much a personal choice. These bulbs are entering the blue light spectrum and, in my opinion, are extremely functional and look great.
Best of luck