Backpacking certainly is a great adventure and a special experience, however I would like to warn you that it's not magically going to cure you. At least, that's my opionion that I got from my own experience and from other people's experiences. When I went backpacking last year I saw it almost as some sort of 'last resort'. However, I learned from it that no matter where I will be and whom I will be with, my mental ilness will be present and I will still feel sad. Maybe not as bad as at home, and maybe not all the time, but backpacking didn't make my headspace all comfortable and coloured. I did learn a lot, I enjoyed myself and it was an amazing experience so I would recommend it. But I wouldn't recommend it as something to change you forever and fix all your problems. And for what I've seen from other people, people do tend to come back as a 'different' person but slowly this will wear out and they fall back into being who they were before they left because they come back to the same exact environment. The experiences will probably make you a richer person but it won't fix you.
Anyways, that is my opionon on the 'not feeling too well' part. As for planning and staying on a trip I would recommend thinking abut what you want firstly. Are you into culture, mountains, the beach? Then google for countries that are full of that what you love. For me it's mountains so I went to a place where they have great mountains and great treks. What made my experience great is that I didn't plan much in advance so I was able to just go with the flow and when you go backpacking you will naturally meet other people and come up with a plan. I worried about this in advance but once you get there you will understand, it will naturally happen. As for staying on the trip, it might help to set out a time for yourself. How long can you afford to be away from home? Money- and timewise.
Hope this help, hugs.
