First off, I am not defending your ex, but some people, myself included, have a deep distrust of doctors. That may be part of where he's coming from.
It may be possible for you to modify the order as far as visitation, but that would require either cooperation from your ex (not happening, it looks like), legal advice (not affordable, it looks like), or you to represent yourself as an attorney. This is a huge undertaking in time and energy, and if your ex gets a lawyer when you have none, you may be up a creek.
Best thing I can tell you for now is to be there for your DS and be supportive. If your circumstances change, check into modifying the order for visitation only. Just because you have shared custody doesn't mean it's a cookie cutter arrangement. You should be able to modify it to a different arrangement without going whole hog for full custody. Full custody requires that you prove he is unfit for shared custody, and it is up to you to prove his unfitness, not him to prove his fitness.
In the meantime, be the best you can for your son and help him through. Let him know there is someone there for him if things get tough with his dad, and work together to discover some coping skills for whatever difficulties he may have.
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Please Don't Tap On The Glass!!