Take a deep breath. Hold it for 4 seconds. Exhale for 8 seconds and take another deep breath. Good? Ok, lets break this down.
First, there are a lot of reasons why you may not be waking up on time. Being sent to a neurological sleep specialist isn't a bad thing. He may actually find what's wrong with you. A little personal story:
I've been treated for insomnia since 2011. I had a sleep study done in 2015. I've been on enough drugs to tranquilize a baby Elephant and I'm still standing. There were occasions where I would be up for 100+ hours, be seeing stuff, and the doctors would watch me take my sleeping medication and then when it did nothing to put me out utter the phrase "That's not possible" Sure enough, a different psychiatrist looks at everything in my records and says to me "Well, the only suggestion I have is that we start over"
So, he changed up the cocktail of medication, did little to change my sleep patterns did a lot to mix up my day time anxiety and depression. Then he says "you need a sleep study" My reply: I had one. He was actually really cool about it when he said "Yes, I see that, but I'm ordering another one, lets just see."
Turns out. I have sleep apnea. The test in 2015 was just good enough that it didn't trigger a positive result, but the civilian doctor when he looked at the results, he went digging through my records for my retest results. I told him there was none. He said if those results had appeared in his clinic, it would have been another night for testing. After my test with him, I got diagnosed with sleep apnea and now have a C-PAP and let me tell you, night and day.
Why is all that relevant to you: your neurological sleep specialist may find something just wrong enough with you that he can make a small change and fix it. Maybe its a change in the lights in your living space, maybe its waking up to a light vs an alarm clock, maybe its medication. Whatever the solution, you won't find it until you work with the doctor.