I grew up in such a household and I can relate and the truth is, it depends on what you put into your healing. Some people don't heal because they just feel overwhelmed by what they experienced. Others get that spark that turns their anger around into something productive where they can throw that energy back into themselves and focus on healing.
I did eventually heal from all of it, but it took a lot of time and effort to build myself up. I spent a lot of time meditating, journaling and releasing all of the "old stuff" to make room for a new way of thinking and being. I am very at peace with my life today and have made a conscious decision to no longer live in the past and I have self-esteem now that I never would have thought possible at earlier points in my life.
Ultimately, the mind is a powerful place and when we take charge of our thoughts and feelings and learn to manage them instead of allowing them to be in charge, it is possible to heal from all sorts of things.