Well, I think the reason why you may be feeling this way is possibly due to being more isolated than other teens who attend public schools. What you're going through isn't uncommon for homeschoolers, but there are ways to improve your situation. I think it's great that you found an amazing girl to date and stay in touch with. Something to keep in mind while you're dating, is to be social with other people so that you aren't feeling so lonely when your girlfriend isn't around. Often distraction is the key; getting out more and being around different people can help take your mind off of feeling depressed & alone. One idea you might consider, is to join a community youth project or club in your area. You could research volunteer groups for your age bracket, or 'organizations for teens', to see what might interest you ~ there are literally dozens of options online.
Getting busy on the social scene isn't easy for people who are homeschooled, but it isn't impossible. If you're with a particular online program, or academy for homeschool, speak with your parent and/or homeroom teacher about local outings that you could attend. Ask your parent or learning coach, about what options are available for field trips. Another idea you might consider, is joining a family gym or fitness club. Some family gyms/clubs offer teen activity groups that allow you to socialize and play sports on site ~ it's a great way to get your exercise for any of your P.E. assignments, and it's a good time.
Stay focused on your future; something that you have to look forward to is getting your drivers license! This will give you a lot more freedom, and the ability to get out of the house more often :)