You are in a tough spot, and many commercial pilots have faced the same dilemma.
Up until very recently, current or recent depression or use of anti-depressants was disqualifying. Once treated successfully and off meds for a period of time (usually six months) you could get a medical, but would typically require a special psychiatric review.
The FAA just changed the policy to allow those who are no longer clinically depressed, but still on meds, to hold a medical. There is a stabilization period and a review of course but it should be allowed.
However...everything I just said applies to the FAA, not necessarily the airlines. Different airlines have had different medical standards in the past, some of them rather draconian. A documented history of clinical depression might even keep you from getting hired at certain airlines.
Non-airline pilot employers normally just want to see that you have a medical certificate, and don't ask any questions. Some airlines (especially the ones you don't want to work at) take this approach also.
So, what to do? First off your health is way more important than any career, especially an aviation career. Do what you have to do to get better.
Also for aviation career purposes you will need to determine whether you condition is situational or chronic. If it is situational (ie caused by specific life circumstances) you can probably treat it one way or another, identify what triggered it, and get on with your life and career. If it is chronic, ie you are just physiologically more susceptible than most people, then a flying career might be tough since you may need constant or occasional meds. I'm no expert, but I would guess if you are a typical soldier that you do not have a chronic depression issue...that would probably show up in boot camp.
With that said, there are a variety of treatment methods for mild depression (other than the typical SSRI's) which might be worth trying...
St. Johns Wort: Herbal remedy, you can get this at the drugstore, and it works for many people. It's very commonly used in Europe. It is like an SSRI in that it takes time (often weeks) to really take effect. It will make you sunburn easily though, so if you are doing field duty that might be an issue.
Diet: Lay off the booze. Seriously. This is huge, moderate or greater quantities of alcohol burn up serotonin...lack of which is usually what causes mild depression. A healthy diet can't hurt either, especially omega-3 foods.
Stress/Anxiety: This can be a vicious loop...constant elevated stress levels burn serotonin. Lower serotonin levels can cause depression and anxiety, which continue to depress serotonin levels. Even if the original stress factor is gone from your life, you can get stuck in a loop.
Exercise: Daily aerobic exercise (45-60 minutes or more) stimulates serotonin production. Again, this takes a little time your levels will actually drop at first when you ramp up your exercise but will stabilize over time. Non-aerobic (ie weights) won't work, and 20 minutes three times a week won't do it either.
Google is your friend...there is a lot of info out there. But again, if you need help or have thoughts of violence, suicide, etc go see someone immediately.