Please, please, please do not see yourself as "a problem child". Let that self-image go. My mother grew up with that and never really started tackling the whole issue until she was well into her 30s and now in her 50s, STILL has major self-esteem issues. Start tackling this NOW so that you can have a future where you feel good about yourself no matter what your life situation is.
You have not screwed up your life. Just like some people take longer to walk or to talk or to read, others take a little more time to "get it" and get things moving in the direction they want it to. You are fine. My own great-grandmother didn't get her high school diploma until she was 80. :) When I was in university, I met people who were attending for the first time who were in their 40s. Things are not screwed up. They're just not the "standard". You're only 20. Life expectancy for females is something like 75. You've got another 55 years to go!!!! Lots of time to make a great life. :)
You should definitely look into a formal GED class, if you can afford it. If you can't, your library will have resources and there may even be other options available if you ask around where you live, even perhaps a high school diploma program rather than a GED. You don't even necessarily need the GED to get into college. If you can take the SATs or some other standardized test for the subjects you want to study in college (or need to have to get in), then you can see where you're at and maybe learn the stuff on your own. Then, when you feel ready, go take the SATs again. Unless, of course, the college you want to attend accepts the ACTs instead of the SATs. (Something to look into!) Which has me thinking about this: go to a local community college and ask them about getting in--what you need to learn, what you need to do. I'm sure someone there will be able to tell you what needs to be done to get in. It's okay if it's going to take you another couple of years. I met this one guy who at 28, was still working on his first degree--he'd changed areas 3 times, took a year off here and there. Just keep working on reaching your goals and you will get there.