If you think you will actually move across the country, then go for it. Find a job, move, make the leap all at once. People do it everyday (not me, but people).
However, if it's not something you are going to follow through on, you can still make changes. Start taking more responsibility at home. Make your self a list of the thing you should be doing at home (cleaning, cooking, etc.). Stuff that you would have to do living on your own anyway. Once you get a routine established, make a bigger change. Find a job, full-time work. Don't be afraid to apply for jobs that you don't think you are qualified for. You would be surprised, some company's are willing to train a person with little work skills. Next, once you have a job, then look into helping out with some of your mom's bills. Groceries, cable, even paying her rent. Again, the stuff adults do every day. All of these things will help you build the confidence you need to go out on your own.
I'm sure part of the anxiety comes from simply having a mom who has spoiled you. I was not spoiled, however, I lived with my parents until I was 27. It was mostly for financial reasons, plus, I was going to school for several years, but I had huge anxiety problems after I graduated and moved out. I found a job 2-hrs away, was going to be living by myself for the first time ever. I had panic attacks in the month leading up to my move and for the first several months I lived alone. But it was really just because it was so different. For the first 3 months, I told myself every day that I was giving it a year, if I was still anxious all the time, there was nothing stopping me from moving back (except a little pride about being 27 and still living at home). You know what, after a few months, I couldn't imagine living any other way. I found I loved living on my own. I still visit my parents frequently. I've always been close to them, I like seeing them on a regular basis, but I have my own life now. I have an apartment, a job, yes...adult responsibility, but I will gladly take the unfun stuff (bills, cleaning, bills, bills) with the fun stuff.
It's not that some people have willpower and some don't. It's that some people are ready to change and others are not.
My progress pictures