Occupational therapy can treat many aspects of SPD. Schools often have OTs, but I would recommend a private evaluation if your insurance covers it (most do). Usually you just need a referral from the pediatrician.
Occupational therapy usually involves devising a "sensory diet". The thing about SPD is that it manifests differently in each person. Some are sensory avoiders, others are seekers. And different stimuli bother them. So OT allows you to figure out what your child's triggers are and then gives you a plan for dealing with them (this is the "diet").
From what you've described, it's hard to say whether your son's behaviors are related to SPD or anxiety (or something else). I would talk with your pediatrician and ask for a referral for an OT evaluation. I will warn you, however, that you may need to be fairly insistent. SPD is a relatively recently recognized phenomenon and many docs who aren't keeping up with things know little about it. You could also google children's occupational therapy centers in your area and get more info from them. They often provide a free screening, which isn't sufficient for your needs but may help you get a referral.
Realizing my DS's SPD was incredibly helpful to understanding where he's coming from and how he experiences the world. Even if your son doesn't suffer from SPD, it would be useful to rule it out.