You should feel absolutely no shame in seeking help for you problems. Mental health issues are as serious as anything else, but they get stigmatised because they can't immediately be "seen". The problems you have faced are horrifying and the human brain is simply not "wired" to deal with these sorts of things- so eventually a short-circuit occurs. Continuing to try to act in the same way people who have not been in these sorts of situations act is akin to trying to walk on a broken ankle- you might be ale to do it, but you're constantly moving in a way that allows you to compensate for the injury, which in turn can mess up all sorts of other things. As with the broken ankle, proper medical care is essential to healing. You wouldn't say that someone seeking help for an injured ankle was admitting defeat, you'd say that they were doing the obviously correct thing- acknowledging that they did not have the training and expertise to properly treat themselves. (It wasn't all that long ago that people did used to treat broken bones by themselves, and would only consult a doctor in case of dire emergency.)
I've had problems of various sorts since I was very little- I would say 8 or 9, starting around the time that my parents got divorced. The family I come from doesn't "believe" in mental disorders, which means that, despite the fact that I knew from that age that there was something wrong with me, I was consistently told that being unable to deal with it myself meant that I was weak (a common argument among people who don't understand these sorts of problems). As a result, other than a couple of "desperation" moments, I never sought any kind of help until I was in my thirties.
I strongly recommend that you go and see a doctor who makes you feel comfortable. Make sure that they listen to everything you have to say and tell them everything that you think might be related, without worrying about how everything connects. If their answers don't ring true to you, get a second opinion. I let my GP diagnose me at first, she decided I had anxiety and depression and put me on medication that made me worse. I felt at the time that she wasn't listening to me, but I figured she was the expert. Now I realise that she clearly wasn't- she was a general practitioner with no psychiatric training who equated what I was going through with the mildly stressed/ depressed clients that she saw every day.
The same goes for treatment. Give everything they recommend a chance for a couple of months, but if it's really not working for you, speak up. Meds will always have side effects and there will always be parts of therapy that are annoying/ painful, but you always have to be asking yourself if these things are working to reduce your depression and make you better able to deal with the realities of day to day life.
It's only in the last couple of years that I got a proper evaluation. I'm on better medication now and can suddenly experience the world in the way that a "normal" person would. Plus, of course, the fact that I now understand the disorder that I have allows me to gather more information and figure out ways in which I can help myself deal with it.
The decision you're taking is a big one and learning to deal with your past and how it has shaped you will be a lot of work and will be a big commitment, but your daughter will thank you for it and you'll thank yourself. It is absolutely worth it.
Here's a web site I discovered when I was trying to find out more information on drug treatments for mental disorders that was a huge help:
Crazy Meds! The Good, The Bad & The Funny of Neurological Medications
There's a lot of serious science in there, but it's written in a super-accessible way from the point of view of people who've spent a lot of time in treatment. Good luck and stick with it. Taking the first step is the hardest part.