I can confirm the headaches likely being due to caffeine withdrawal as I once had this problem (and I was only trying to give up caffeine, I wasn't doing Atkins then!) The headaches went away after a few days. And I wasn't drinking a lot of coffee/cola to start with, so you don't necessarily have to be taking in huge amounts to get withdrawal symptoms.
On the other hand, those headaches behind the eyes etc sound to me a lot like "sinus headaches" ie due to infection of the lining of the sinus cavities, which are located in the facial bones above and below the eyes and also in the lower back part of the skull. I once had such bad headaches there, I couldn't find any painkiller strong enough. It turned out to be a sinus infection, cured by prescribed antibiotics. Have you had a cold, sore throat or similar recently? Go and see your doctor if they don't go away very soon.
Good luck!