I am new here too. I am a registered nursing lecturer with a lot of experience in mental health in particular all the variants of schizophrenia. You have my full sympathy in what is a dreadful illness.
Our church advises that all 'worthy males who are capable of serving a mission , do so'...that means if you are not capable, then you do not need to serve a full time mission, though there may be other ways youcan serve if you wish and it is agreed.
One of the most important therapies for those with a psychosis is to be involved in activities. Many of my patients have joined college classes that suit their needs or clubs that have a project or they do voluntary work suitable for them.SO, it may be possible that you could serve in other ways.
Some of your anxiety about serving could be because sometimes this illness when the person feels a bit better, makes them think they are capable of more than they are and it is ok to accept this and take a step back and not feel guilty.
Of course you need to speak to your bishop, stake pres and your doctor and the church also has its own doctor. You said you dont trust your bishop or stake pres. without making a judgement on you, and knowing that no one is perfect even priesthood members, could it be that your perceptions of these two people is skewed by your illness?
maybe someone you do trust could go with you , someone who would understand you and help put yoru feelings across if you find your own mind going in circles as it can do.
I hope that you find peace and comfort in whatever decisions you make.