I truly understand how you would feel about this "being a weeping prophet and all". But if I had to choose I would do what God called me to do even if it means being a weeping prophet. In my eyes I wouldn't call Jeremiah "Depressed", he just cared truly about God's people. Jeremiah is no more a weeping prophet than Jesus was/is. The shortest scripture in the bible is "Jesus Wept".How about a really strong avoidance of one particular prophet? I have never read the Bible all the way through consecutively because I can't get through Jeremiah and Lamentations. I've told people this before. I don't know what there is about Jeremiah but I get so emotionally involved when I'm trying to read through that I always quit. There's something about his heart bleeding for the people and the fact that nobody would listen to him, and God told him not to pray in certain situations because His mind was made up. Jeremiah just seemed so hopeless. Pain upon pain.
A few years ago I joked with someone I was afraid I might be a "weeping prophet" because God seems to share His sorrow with me. They convinced me that if I was getting closer to God I should be experiencing joy, that overwhelming sorrow is not from Him. So I ran -and avoided reading Jeremiah fearing "this way depression lies." And I've already spent many years drowning in depression.
And if God called you to care for his people like "he does", I don't think God would place such a heavy burden on you without giving you the proper equipment (the heart,patience, endurance, and the ability to be strong).
Let's look at the prophet who didn't want to go to God's people (JONAH) and I am not saying that is exactly on what you are doing. But whenever I hear people say that are scared to do what God called them to do or just not wanting to do it that is who I think of.
Intercessor are also Great.... We all need them. Jesus makes Intercession for us, the holy spirit is a intercessor!! Wow if God is calling you to team up with Jesus and the holy spirit to make intercession for certain people then........ Go for it!! Let God GLORY BE SEEN THOUGH YOU!!!