The loss of a loved one sucks, and depression is natural and your bodies way of mending. You can't rush it or run from it. Never make someone a priority in your life if you're only an option in theirs.
And don't try to be friends, it only drags out the pain and suffering. Get rid of anything that reminds you of them, lose their number/email/im/whatever. Time makes everything better and eventually they won't cross your mind so much, if ever. Just be happy with yourself.
Yes you should breake up with him because in both situation you will be hurt. Be strong and find new bf who will love you. I'm in the same situation and I did it but still I didn't find gf.