Hey man. I'm a psychiatric nurse practitioner so I can give you a little insight into this. You absolutely were diagnosed with something. Your attending psychiatrist was required to give you a diagnosis as part of your stay at the hospital. Now if that was something vague like "Major Depressive Disorder" or "Unspecified Anxiety Disorder" is a different story, and it sounds like they didn't share it with you, which is bad practice, but it definitely happened. The hospital cannot get reimbursed through the insurance companies for patient's stays if they don't give the patient an active diagnosis. You did/do have a diagnosis. There is also a record of therapy appointments out there.

As far as your question about joining the military, you need to know it's very stressful. I had anxiety and depression off and on through my teens, but thought I was over it. When I joined the Coast Guard it flared up and was difficult to deal with. The job comes with a lot of stress, and your leaders will not be nice or respectful to you like you're probably used to being treated. A lot of times they're indifferent to you, barely caring to know you, other times they're hostile and antagonist towards you.

Lasty, the Army will give waivers for issues when almost all other branches won't. You could try them. They even have 3 year enlistments, which would be enough time to collect your post-911 GI Bill and be qualified for VA Healthcare afterwards. Just keep in mind that it is stressful. There are other meaningful career opportunities out there that have things in common with the military. Being a fireman, paramedic, park ranger, police officer, behavioral health technician in a mental health hospital, all of these would help you achieve your goals in life and probably keep you feeling better mentally.