i'll try to look for a neurologist as well, hopefully the answer is right around the corner.
Because you've had a past diagnosis of depression/dysthymia, and given your age, you might have a hard time getting a referral to a neurologist for what you call "brain fog". And even if you do get a referral, the referring doctor may likely write a report for the neurologist saying that your cognitive problems are likely psychiatric in origin and a complication of long-term refractory depression, given that depression can cause cognitive problems, particularly if it persists long-term without abatement. So, you might have a fight on your hands just to get a neurologist to even consider that it might not be depression. When presented with symptom clusters in a young person without concomitant neurological symptoms like problems with coordination, etc, they are likely to deem it psychosomatic in origin. If you're lucky, you might convince one to order an MRI and an EEG after he quickly checks your reflexes, the ability of your eyes to track movement, and perhaps gives you a worthless MMSE. Often, the general practitioner will refuse to make any referral to a neurologist for someone complaining of mental symptoms along with fatigue, as general practice guidelines recommend that the family physician first refer to a psychiatrist who is supposedly more skilled at determining whether a neurological screening is appropriate.
If you have a psychiatrist, they sometimes will order brain EEG's or MRI's to rule out structural anomalies or seizure disorders if a patient is insistent. They are unlikely to be willing to order any other testing to check for organic disorders that can cause brain fog, other than basic blood work and STD testing, as it is not conventional for psychiatrists to do so, except occassionally in in-patient care in a mental ward. More often what psychiatrists in combination with a psychologist will do is force you into talk-therapy where they will pick at you until you tell them of some troubling event in your life such as a repressed memory of sexual abuse, physical abuse, or humuliation, and then convince you that all of your physical and psychic complaints are a result of your life experiences.
You can go to a neurologist without a referral if the particular neurologist takes such appointments, but most insurances will not pay without a referral.
There is also a type of doctor called a "neuropsychiatrist", a doctor with certification in both psychiatry and neurology who specializes in differentiating between neurological and psychiatric disoders, or uncovering combinations thereof. A neuropsychiatrist might be the best choice in your case, and you might have an easier time getting a referral. There aren't many of these doctors however. You might have to travel to a nearby large city if you don't already live in one.
Personally, if I were you I would press for an FDG-PET scan of the brain, as MRI's and EEG scans are normal more often than not in someone your age presenting with "brain fog", and functional brain imaging is much more likely to show a problem. Ironically, only MRI's and EEG's are likely to be ordered, though, despite the fact that they are statistically less helpful in finding problems in a young person with minimal cognitive impairment. In your case, insurance likely would not pay for functional brain imaging. A SPECT scan is less expensive than a PET scan (costing sometimes under a thousand dollars rather than several thousand dollars), but it's not as sensitive as PET or (f)MRI. Another problem would be in finding a doctor who would actually be willing to order a PET/SPECT scan. Some neurologists/neuropsychiatrists would be willing to, but perhaps a minority. There are centers in the U.S. that order these routinely for someone complaining of these symptoms, however. You can do a web search.
As for blood work, ceruloplasmin levels can be checked to rule out Wilson's, you can have testing for certain viruses or lyme's disease, etc, but the chances that any one of these will turn up anything is fairly low, which is why doctors don't usually order them unless there are more telling symptoms other than the not uncommon complaints of brain fog and fatigue that the medical establishment believes is usually the result of depression where basic blood panels and nutrition are normal.
In summary, because a large percentage of people with long-term depression eventually report vague cognitive and physical symptoms like problems with memory, slow processing, bad executive skills, fatigue, unrefreshing sleep, etc, the most likely diagnosis often attributed to such symptoms in a young person without more telling symptoms is "depression."
Personally, years ago when I worked third shift I had many of the same complaints you have. Despite the fact that I got usually seven to eight hours of sleep, falling asleep after 5:00 AM and waking up in the afternoon caused me to feel confused, be depressed, and have some other vague cognitive complaints. After finding a new job with better hours, I began going to bed every night at 11:00 and getting up at 7:30AM, and all of my symptoms resolved with a couple of weeks. Circadian rhythm disturbances can definitely cause problems in people susceptible to such problems, and the time at which a person sleeps can be just as important as how long he sleeps. For some reason, some people are much more sensitive to this than others. It may be associated with different genes regulating sleep-wake patterns, melatonin, exposure to light etc. Quite a number of published studies establish that irregular sleeping patterns can lead to an array of depressive and cognitive symptoms in otherwise healthy individuals.
I would step back and evaluate how you live on a daily basis and see if any of it may be contributing to how you think and feel. (1) If you have a tendency to oversleep, undersleep, sleep at the wrong time. (2) If you have a tendency to what I call "vegetate"; in other words, spending long periods not doing anything to engage the mind or body which can lead to psychomotor retardation. (3) If you are not having significant social interaction. (4) If you are not being active physically and going outside, getting plenty of sunlight, etc. (4) If you might not be getting enough sunlight (seasonal affective disorder). (5) If your symptoms were preceded by a period of despair, active depression, trauma, etc.
Finally, you need to consider that after correcting any problems in your daily lifestyle, that it may take a few weeks to really start feeling a difference after improvements are made.