Homeschooling with your lack of confidence would make you more likely to be even more of a social outcast.
I was raised on Homeschooling and I socialize very well in that field because it's where I have the most experience, whereas if I switched to public schooling I would probably have a harder time doing it. Switching schooling methods isn't the answer. Your issue is primarily more psychological and preference based. It sounds like you would prefer for friends to come to you rather than you going out to seek them.