What is the right path to deal with depression?

The best way to deal with any medical problem(and depression does fall into this category) is to seek professional help. The Army's officer in charge of the effort to deal with this sort of problem is a general officer who freely admits that he struggles with post traumatic stress and depression and is currently in treatment for this problem. The point is that the Army appears to be getting to the point where it realizes that mental health is a subset of overall health and treating it as such is beneficial to the service and service members. So follow your buddy's advice. Get professional help now.

The right and only path is to seek help. Tomorrow after your work formation, you need to pull your team or SL aside with your PSG and talk to them. Request to seek help that day. Go and see the chaplain or health clinic. If you feel the need to talk as bad enough, you might even consider morning sick call. Don't delay and let these feelings fester.

In general (each commander being a human and thus having different opinions) . in general seeking help for depression is not an issue..If the medical determination is that the depression cannot be addressed with moderate time and therapy it MIGHT lead to an administrative discharge, but in no way required.
If it is found to be clinical depression where you are likely to hurt yourself or others, it could effect clearances now, or in the future.
But end of the day, its not going to go away on its own, so deal with it, deal with 2nd and 3rd order effects later IF they even come up.