I don't think you are in denial. Your child may have SPD, or your your child may just be responding differently to some internal or external change. Diagnosis are very subjective. People have pet theories, or get can get stuck in rigid "proven" diagnosis.
I think you should absolutely trust your instincts and observations. Sometimes kids just need a break. Normal has become very narrowly defined these days, it seems.
You should ask the teacher for a detailed description of what she is observing that concerns her. It may be that she is picking up on something that is apparent in a school environment, or to her because she is tuned into something. It could also be that she just has an unrealistic expectation that kids should always be able to do whatever they are required to do, at any time, and if they withdraw, there is something WRONG, rather than something wrong in the immediate sense.
It is important to consider that your that your son may be very comfortable with you and your mom, but that he may express distress in the school environment, so you don't see it, although it is curious that the other parents don't see it either, but they often don't see "it" when something is really wrong.
Unless your child needs urgent medical care, don't let anyone do anything to him that worries you, unless you get a good explanation and you feel it makes sense. Therapists can help, but thay can also harm. So trust yourself on that too.
3 is an age of big changes. Kids are constanly revising their understanding of their place in the world and in relation to everything.
Maybe circle time is after snack and your son's stomach is bothering him or he feels a need to go to the bathroom. I would investigate the details and see if there is a pattern of withdraw which indicates sensory defensiveness or something else. You may even want to hold off on the OT until you have a better sense of what he might need it for, since it sounds like there is an absolute limit on the number of sessions your insurance pays for.

---

I second the suggestion for a ped neurologist, although they have pet theories too, they can at least look for any indications of a neurological issue.