Medical Discharge for Depression?

Hi I'm currently in the Navy as a Corpsman and I've been developing depression for about 6 months now. I'm currently on my 3rd type of med's trying to get it fixed but nothing is working. I've been failing at work and can't seem to do anything right and finally agreed with my psychiatrist that If I were out things might get better. He has recommended I get discharged. My main questions are this. Will it be a medical discharge or administrative? How long will this process take? Does anyone know if I will keep full VA benefits and the GI Bill or Post 9/11 Bill? Please do not leave responses about sucking it up and finishing out my contract. I wanted to serve and I am proud doing it and I hate that I can't go greenside because of my problems right now. Any HELPFUL responses will be greatly appreciated. SEMPER FI and SEMPER FORTIS!