What is the best type of doctor for Narcolepsy?

Have you seen an endocrinologist for evaluation of all your hormones? You may have low thyroxin levels, just as a fr'instance.

Neurologist who specializes in Sleep disorders

You will want a psychiatrist with a well known reputation for treating such. It is one of the harder diagnosis to officially get. Mainly because your going to have to spend some time trying lessor meds before they generally agree. I have sleep problems that mimic narcolepsy. I use to travel a lot and would find myself at rest areas and hotel entrances waking up from a nap. It got so bad I ran off the road twice. Thankfully a huge car it bounced off the temp cement divider and the barrels and I woke up both times before going off the freeway it may of been more I remember being startled awake often. I also have Adhd so I think you will find your DR that also practices in that area. The meds are similar and it's almost 2 sides to the same coin. I tried Armodafinil marketed originally as a med for swing shift workers. My experience was that it will wake you up like very few other meds but for me it was short lived as in 8hrs and I dropped but that was lack of sleep kicking in I think. I was trying to get away from over 10yrs of Adderall which only comes generic now as amphetamine/ Dextroamphamine sorry can't read the bottle but once the dr is comfortable that is what you need it can be prescribe 3x daily so you have some control Adhd medication. They prefer to issue the non amphetamine which falls into a different class that your Concerta, I can think of the names but they are slow release all day long which doesn't work for me I need the immediate go and then anything else interferes with sleep eg the first med I listed which is my go to I can't after noon anymore. Everyone has different experiences to meds but just given 20yrs of living it. I think you when your looking for a dr you wont find just narcolepsy or look for adhd with narc also listed once they see either of the meds are safe for you they can start you on a low dose bc daily I range between 20mg and 60mg have been doing it for so long even the immediate release will build up and I need to be on almost no dose for 2 wks until it washes from my system or I really have sleep problems as in awake for 48hrs straight not even resting my eyes. I hope I gave you some avenues to look down and some meds to research so you know what to suggest if you end up with someone with no experience in your area. Good luck.