I think that before you start suspecting SPD you need to address things like diet and interaction.
My little cousin is a funny little man. He's 2, nearly 3, and he was going to be medicated for severe ADD. At 3!! They cut out all crap from his diet, he's on veggies and healthy food, less telly, lots of playing with mum and outside time. And he is now the tamest little thing. He just needs interaction and less junk food.

Maybe something to consider?