Its too bad the nurse was so discouraging. It was finally a nurse who convinced me to go ahead and pursue guardianship.
Is your son on meds, and followed by a psychiatrist?
Has he had several hospitalizations with repeated med-noncompliance?
Has he been evicted from multiple places or been threatened with eviction?
Is he able to shop for himself (sounds like you have to take him)?
When he is ill, does he put himself or others in danger? That is a tricky one, you have to make sure you can word things in a way to show that.
Since he is on SSI, it seems he is considered disabled, and unable to work.
Even if your son does not allow the doctor to talk with you, you can still speak with the doctor, and generally they will give some sense of how things stand - I found that support of guardianship from his doctor was absolutely the most important thing for getting guardianship.
And of course, if your son is cooperative, and agrees to guardianship, it would be much simpler.