I was in the army 5 years active duty before I knew about my Asperger's. If you're on a large base there should be a mental health clinic there (at Ft. Hood it's called 'Mental Hygiene Clinic') by the med center. Just go there and say you'd like some counseling. There's confidentiality, so you shouldn't have to worry about them calling your unit. I'd be careful about saying outright, "I want to be diagnosed for Asperger's" since it'll sound too much like you're trying to get yourself out of the army early, which they'll try NOT to do. But if all of your symptoms match the criteria then it'll be hard to deny when it's in black and white in the book.
Turning your diagnosis into a discharge is another matter, one I'm not qualified to give advice on. You'd have to show that it's NOT in the army's best interest to keep you around, and considering the screw-ups they DO keep around, it'll be an uphill battle. Honestly, if you have 3 years in, you should be close to your discharge date anyways, I'd say just ride it out and get your honorable.
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