It's true that some of the original research on the success of low carb diets came from doctors researching epilepsy but I want to be sure you're not also managing epilepsy. can you clarify?
I've not found doctor's knowledgeable on low carb diets. best to educate yourself.
the stomach burning is something else entirely. suggest you get a sigmoidoscopy and ensure you don't have gastric reflux. that I know a lot about. some folks with GERD do find that their stomach produces more acid when on low carb diets. there's a book on the subject called 'Dropping Acid' by Jamie Koufman and Jordan Stern (both MD's), you might want to pick up a copy but they are not low carbers they deal with acid reflux.

Thanks. No acid reflux here. No epilepsy either. Never had regular stomach burn except when I was pregnant. Overall, I am pretty healthy. The only reason why I would like to be supervised is because there's a bunch of tests that can be performed that can be useful to track progress. Plus, frankly, I don't want to mess with my metabolism without having the opinion of an expert.

As long as you're eating a sufficient amount, this way of eating shouldn't really "mess with your metabolism." Also, keep in mind that doctors are human, too, and prone to all things human (including ignorance and arrogance), as well as the fact that general practitioners know next to nothing about nutrition. A well-read patient is often more informed than the doctor.

That said, if you really want to find a doctor to "supervise," I recommend looking for holistic or functional medicine practitioners. These doctors will be more likely to be open to alternative ways of eating and even if they don't know about something, they'll be more open to learning about it. You might want to start with http://paleophysiciansnetwork.com/ or http://primaldocs.com/ , because while you may not follow the Paleo way of eating, the doctors listed there will be more aware of, and open to, alternative/unconventional diets in general, and won't be dismissive of you and treat you like you're a heart attack waiting to happen. If you're open to it, you might want to also check out a naturopath, at least in addition to your current general doctor (if you have one), since they generally focus more on diet and lifestyle changes as a means to better health, as opposed to just piling on prescription after prescription.

As for your "stomach burn" (is that another way of saying heartburn, or is it something different? I've honestly never heard of stomach burn), you might want to make sure what you're eating doesn't lean too far on either end of the acid-base scale. Remember, your stomach is a tank of acid that dynamically adjusts based on what you eat. The alkaline foods will neutralize part of the acid in the stomach, requiring the body to make more. Unfortunately, some people don't make as much as they should, which is (ironically) often the cause of heartburn and its ilk ( http://www.stopthethyroidmadness.com/stomach-acid/ <-- while most of the article is specific to hypothyroid issues, there's still some good stuff on stomach acid and its issues in general). Play with the specific things in your diet, such as eating less alkaline foods and more acidic foods, and see if that makes a difference in how you feel.