Hi Linny
Congratulations!!!! Firstly about the clear blue stick, you never get false positives, if there is HCG (preg hormone) in yr wee, then the stick will detect it when it gets to a high enough concentration. You only get false negatives due to the level of hormone not being high enough for the test to detect it.
As for diet, as a Doctor I would recommend that you eat a well balanced diet, and take Folic acid daily plus you can take pregnancy supplements and fish oils etc for brain development. I think your own doctor will tell you the same, I'm not away of Atkins/low carb/high protein and being pregnant so I can't comment further on following a low carb diet. Although I'm a huge fan of LC diets, I personally wouldn't do it in pregnancy but that is just my own opinion. You need to gain fat near the end as this is used for breast milk etc and glucose is a baby's main fuel during the pregnancy and for growth of the baby.
You can always return to LC in the post natal period if your not breast feeding, again you need high calories to make milk.
Hope this helps :0)