You will be fine. Actually, you'll be a lot better, once you get things straightened out. I know people on anti-depressant medication that have their CCW permit, and were on it when it was issued.
Depression is a funny thing, because it's so misunderstood. Many people don't understand it, and dismiss it as something you can just "snap out of". It is a very real thing, and can be debilitating. It can control you, and methods of self-medicating (alchohol, drugs, etc.) just make it worse.
Many men will go untreated because they don't want to be labled defective, or feel like they are less of a man because they need medication to feel "normal". The funny thing is, it's really no different than people that have heart conditions, diabetes, and other medical conditions that require medication. You take medication because you do have something wrong, just like anyone that takes any medication. The reason it's such a hard fact to get over is men are raised not to learn to deal with feelings and emotion, and when those things you don't deal with raise up and take control of your life, you keep trying to supress it, and it just gets worse.
Bottom line, if you are fighting depression, get counseling, get medication if it is deemed necessary, and don't fight yourself over it. Noone has to know unless you tell them, and honestly, it's none of their business. Good luck to you!