Hey man, I am probably going to go into a lengthy response because I know how you feel. I actually just got out of a situation where I had an eating disorder that had almost taken my life, coupled with multiple suicide attempts due to very high anxiety/ depression/ self worth issues. And even as of a several weeks ago I did not think that there was a God and that this life is all there is.
Here is the issue about having faith. People tend to think finitely, or in a box, and we naturally go based on what we can observe. So it is obvious that you would have trouble believing in God and in Jesus' existence since we cannot observe it. But keep in mind there are areas within existence that we are not able to observe. Take for example, since the universe expands then it must be finite. But what exists beyond that? Even though we cannot actually observe that or even begin to comprehend that, and regardless, that doesn't change that there is an end. So with that in mind would it really be impossible to rule out that there could be a God that transcends that area of space/time?
With that said, I really recommend you keep on talking to your psychiatrist and BE OPEN! I cannot begin to put enough emphasis on how important open communication is for your treatment. You need to be willing to be helped before you can receive help. And maybe that is what is happening with God. God will not just intervene with a miracle to magically make our worries disappear, because what kind of free will would we have? We are given opportunities by God to change as opposed to divine intervention.
I recommend you through your burden onto God, let Him know you want to find the truth and let it be know to you. Just as Jesus said "Keep on asking and you will receive". People have this weird conception of religious folks because they believe they are only religious to listen to the answer we want to hear. Which is NOT true, we need to realize that God will not give us the answers that we want to hear and there are cold, hard realities that we will have to face in this life.
It sucks man, trust me. There is no "cure" for depression, and it is not as easy as saying "stop being depressed" or "God has a plan" because that is not helpful. What I will say these things to you:
1.) Keep seeking professional help - You do have depression, which is something that is manageable through therapy, coping skills, and prescribed medicine.
2.) Do not think because you are still depressed that God doesn't love you - God very much understands what you are going through and I am positive that it is hurting him to see you suffer. Unfortunately in this physical world we do have MANY imperfections, and one of them is depression (which is a chemical imbalance to make us feel bad no matter what). He is speaking to you, it may not be what you expect though. Hang on, my friend.
3.) Talk to your friends, enjoy yourself, and do what you love - This is also very important. We need to have these things in order to cope through this life. We need to be able to love, to have laughs, and have down time in which we can enjoy ourselves. Do what you love.
4.) Please use this subreddit. I cannot force you but you have no idea how much it has helped me with my faith. I was a very staunch Atheist, turned Deist, now turned Christian and I am at a point where I believe serving God is what I want to do with my life.
Stay strong, brother. I will be praying and thinking of you. This is coming from somebody who understands you. It does get better!