Exactly as you have described - embarrassing random smells and I had absolutely no clue what was going on! I understand what you are going through I really do but hang in there because you will find a cure just keep trying!
I had this problem for 10 years and eventually after many years of seeing specialists I was diagnosed with rectal prolapse, which is basically the muscles holding your rectum and colon are weak (Pelvic muscles) and not holding everything in properly. The solution was to have a section of my intestines chopped out to 'pull' everything back up. Apparently this condition is very rare in young people (I am now 35 and had the op about 2 years ago) which is why it took so long to diagnose.
Definitely worth getting this checked out as a possibility - there is lot about rectal prolapse online, i didn't even have anything coming out of my anus so it can be quite subtle and just be enough to interupt how the anus works.