Taka, I really do know how you feel. I'm also homeschooled, no siblings, not attending co-op, and not going to any churches (since all the ones within a 50 mile radius don't consistently give real, good, Biblical teaching).
Here's my suggestion: Find a sport or activity you'd like to get involved in. There are homeschool groups all over the country, and each of them has their own little Facebook page and activities homeschoolers can participate in. I do homeschool ice-skating once a week (and it's free!). They also occasionally host field trips, etc.
You can also get involved in NON-homeschooler activities -- if you're mentally prepared! I was a competitive gymnast for 4 years, and for all those four years our level of girls became really good friends. Eventually I had to quit, after almost having surgery for a second time. Your parents may not be too keen on this, since (in the words of my sometimes-hyperbolic mom) "Seriously, kids are so messed up these days, there's no one worth being friends with." After a well thought-out and respectful discussion they won't yield, don't press the point. Trust me, it will only make you both frustrated. Just wait for a good opportunity to arise. (Listen for God... He'll give you that chance if it would be beneficial for you to have it!)
I'm currently taking ballet 2-3 times a week. This provides minimal social interaction, since there's no talking allowed. However, sports teach some really good life lessons (e.g. humility, perseverance, diligence, commitment, the paying off of hard work).
*Edited to present tense