I hate to beat it the point, but if I don't tell the military that I've been psychiatrically hospitalized and treated, will they find out anyway? Thank you guys so much for answering this quickly.

Yes, they will find out anyway, and in fact lying on your application can, if they already have you in, cause them to give you a dishonorable discharge ( not a good thing) they could even charge you with fraud of the application and try to prosecute you due to cost of the processing.

Thanks again