Another one who can relate here. One of my children is 2E, and it's always a good idea to keep paying attention for any possible issues, be they ASD, sensory issues, learning delays, whatever. But perfectly "normal" kids can be REALLY full on too... My 2nd daughter is (so far) my most "normal" and she's more highly gifted than #1. She was an easier baby than my eldest, but when I hear other people carry on about the bad day/week/month they are having with their baby I tend to laugh and think "Wow that was an EASY day with my EASY baby. Get a grip!".
My advice to you - do NOT try crying it out with a child like this. When DD#2 was around 2 I (crazily) decided she was not getting out of the cot until nap time was over that day. So I sat next to her for 2hrs and tried to get her to sleep. She stood in the cot and screamed at me for 2 hrs. And then we got on with our day. And she did not nap again for over two weeks. Remembering that this was my easy child :-).
We went to the peds today and DD clamped her mouth shut when the doctor tried to get inside and stuck her lower lip out and slapped the doctors hand away again and again.
The doctor was like "Wow, she has a temper!"
By 8 mths, my youngest was totally picking people's hands up and emphatically throwing them off her if they tried to touch her without permission. She'd dive into the arms of someone she liked though.
I find it exhausting being out in public with #3, not so much fun places like the park, where she is an angel. But grocery shopping for example is AWFUL a lot of the time. I can't tell you how many times I have had that "thank god you've paid, please leave and don't come back with that screaming child" look from cashiers. There is something about how she screams that invites horror rather than sympathy.