SPD can affect children differently. My DD1 has SPD as well as autism and is know to do flappy movements, not necessarily jerky ones.

I would suggest seeing an OT who specialises in SPD or paediatrics. Paediatricians don't all work with SPD, and often I've been told that there is no such thing. OT's are the ones who do the assessments and diagnosis of. Check out online for an SPD checklist and bring that with you to the paed if you want a referral. Check the Autism Australia information out for OT's who work with SPD. 80% of Autistic children have SPD. That is why it is so related.

I had DD1 in at the Brisbane Mater Childrens for an interdisciplary assessment. She had a hearing assessment, speech assessment, OT assessment, Paediatrician assessment and physio assessment. It was very comprehensive and gave us a great place to start from. People who work with kids with different issues including high IQ's find the pieces to the puzzle and put it together.