Getting rid of them is not so necessary as being freed from their power or ‘charge’. There are several ways you can do this, and a counsellor as krillco suggests is one option. My experience is that The Sedona Method is the most powerful tool I have used, with the Work of Byron Katie almost equal in effectiveness. It’s hard to say which is more effective to be honest as I used the Work for several years and saw huge improvements, but since I also learned to use TSM the changes in how I felt about life just soared and continue to do so. The Work tends to focus more on thoughts, and TSM on feelings, but both overlap, which is probably why for me they make a good combination. When I have introduced people to these processes more have taken to TSM.
Very basically, you allow yourself to feel your feelings instead of trying to resist or get rid of them - which is what most of us do most of the time - and then you then let it go. For instance often we hold onto feelings of anger or fear because we think that otherwise the person we feel angry at is getting away with it, or maybe because we feel that we are betraying ourselves if we let go of the feelings.
I have written several hubs on various ways that using TSM can help (though they aren’t titled with that) and one on The Work. Another process many find helpful is Emotional Freedom Technique. I’ve never taken to it but that is probably because I have what I need with the other processes. The Human Givens approach is also very effective, though my experience of it is limited - you do need to see a qualified HG therapist, it’s not something you could do on your own.