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Yes, you should. You should also apply to the VA for benefits.
First, you should file the DD Form 293 seeking an upgrade to your discharge
status. Your disorder was not considered during your characterization of service and could have played a role. Now, you have to understand that these are rarely upgraded, but you have a better argument than most. You'll probably have to apply a few times, but do so because the board considering the application changes and they'll look for different things.
Second, you should apply for benefits. An OTH is not an automatic disqualifier for VA benefits
, for service connected disabilities or general medical assistance. It can be, but is not automatically. So, you would have the ability to have the VA make their own determination, and your psychiatrist's information would be useful in that regard.