OT has been awesome for my son! He is nearly 5 now and has been going since he was just over 3. He has Asperger's Syndrome and the sensory integration therapy has done wonders for him. He still have odd behaviors, but he has come a LONG way in the past 2 years. He has gained physical strength, self-confidence, conversational skills, turn-taking skills, mental flexibility, and much much more while also integrating some of his senses.
My son was evaluated by early intervention just before he turned 3, and then by the school district after he turned 3. He was also sent by EI to a developmental pediatrician who diagnosed him. The school can evaluate her, but can't diagnose (but can suggest a diagnosis). Get the school to do an eval, and then decide from there. We do private and in-school OT (and speech/social skills therapy).
You could also read the book Living Sensationally or Out of Sync Child to get an idea of what sensory issues are. The check list in Living Sensationally will probably be part of the diagnostics uses.
Oh, and my insurance pays everything but the co-pay up to a certain amount (which we have not gone over). Also, if you are nervous about leaving your 3 year old, I sit in on all of my son's sessions.