I came to the conclusion that I need help, so I asked my pediatrician what to do and she referred us to the psychiatrist. She is also referring us for an OT eval.
Our family's experience is that an OT is usually going to come back with suggestions of SPD, whether or not that is the underlying issue. I'd recommend a neuropsych eval to look more fully.
Currently, he has probably 5 of 7 days a week in which he has tantrums up to 15 times a day and the duration of at least one can be up to two hours. He has always had difficulty with transitions. He is driven to finish tasks before we move on, if he sees a cabinet door open and we leaving the house, for example, he can't leave until he closes it. If he is enjoying a song in the car, he screams for us to not turn off the car until the song ends. He loves routine, he struggles when our schedule is off. Order is important to him, he enjoys cleaning his room and taking inventory of his books, toys, etc.
I thought he might have ASD at around 18 months because he was only interested in letters and puzzles (for several consecutive hours). He was always very social and was speaking in sentences and had a vocab of about 100 words at the time so the doctor was sure it was not ASD.
What kind of doctor was that? Forgive my skepticism, but I'm skeptical-- your description here sounds very much like ASD, and I would want to see a specialist.
Our 2E ASD child (Verbal IQ > 99.9 percentile) had no substantive language delays, and yet is very clearly autistic.
I'd seek out someone who specializes in autism and ask them to rule in/out. Make sure they do the ADOS.
The psychiatrist said that he is clearly gifted but I still have those moments when it hits me in the gut (all of the anxiety about his future)and I think, "Maybe we are all wrong?" Many of my friends are teachers in the lower grades and they sometimes give me scary looks and say things like, "I have kids in the first grade who can't do that [insert something academic]."
It is perfectly possible to have a developmental difference and yet be gifted. Even extremely so.
"Overexcitabilities" are IMO too often used to explain away things that would be better dealt with directly.
When the psychiatrist asked about sensory issues, I listed a few things but when I got home, I began to remember: he screamed at every single diaper change until about a year, wasn't into being snuggled, one of his first words was "light" and he obsessed with lights for a year, he always, always, always resists a bath, screamed at every toothbrushing until recently, hates his hair being combed, tells me that he hates certain shirts. One of his first big sentences was, "I want a different shirt". This is all evidence pointing toward SPD.
Or ASD, which embraces these issues plus trouble with transitions, need for order, need to finish tasks, etc. Needing to finish tasks isn't "sensory"-- but very typical of kids with ASD. I'm not diagnosing your child over the Internet-- no one should-- but I do think you should seek further expertise.
We did well to see a doc at a children's hospital autism clinic, one who'd seen thousands of kids and was very well tuned to rule autism in or out. You want that kind of expertise.
Hang in there. It gets better.