Hello i am new to this forum and also am in the midst of getting a diagnosis for my 4/5 year old son who is currently in reception in school.
He shows similar traits to your son and my son shows 3/4 of the traits of SPD.
He is classed as having a developmental/learning/speech delay by his pediatrician and had a few months of speech therapy which helped him a little bit but barely. The speech therapy stopped in summer 2014 just before he started his first year in reception at primary school this September just gone. I deal with the SENCO lady and his class teacher at his school and he is on the SEN list and only gets some help from the assistant teacher occasionally but not the one on one time he needs like he also had in preschool with a specialized assistant the government funded for him which did help him improve alot.
We tried to get a statement for him in school but it was rejected as he was showing signs o improvement which is absurd!!
His preschool teachers were so sure he had a learning disability such as autism but knew he wouldn't be diagnosed with anything as instead of being typically unsociable and withdrawn as a child my son is over friendly and excitable with other children and adults! Because he is too sociable he is being brushed off by these doctors which is extremely frustrating as these learning disabilities/neurodevelopmental disabilities it doesnt class them as "anti social" it should be more that their social skills are different to that of their peers...whether it is being too shy or over confident and friendly with other children!
My son is sensitive to noises and covers his ears, is easily distratced in class and non stop fidgets and moves about! Slow at performing speciic tasks, struggles or avoids fine moto skills and is delayed with these, very clumsy always stumbling, struggles with transitioning resulting in tantrums, his underatsnding is also delayed, and i could go on and on!

He too has a thing for soft blankets and gets fixated on his "snuggles" still as he as an obsession with smelling them and feeling them and if he doesnt get to do that he will have a meltdown.

He too struggles with other peoples personal space aswell as his own! Always bumping into others knocking other children over, talks to close to their ace standing practically ontop of them or sitting on them in ques etc.
Needs to run around or fidget alot but not excessively the running is outdoors.
His attention spam is short, he too struggles to know the difference between hot and cold sometimes.
His pain barrier is quite strong where banging his head and falling when hurting himself can go unnoticed or his reaction to being hurt is delayed.

Lets hope we can get the right help for them as im driving myself insane and just want answers but it is so hard to explain to a doctor/pediatrician who sees and assess them for all of 1 hour or less what they are really like day to day!