Hi OP, I know where you are coming from. I think that most parents, especially mums, have felt like that over the course of our parenting lives.
I have a husband, but I still feel terribly lonely some days - he works very long hours so I'm the one with the kids most of the time in the hols - , more so in the summer, when you spend days on end with the kids, trying to keep them busy and entertained, doing always things for them and very little for yourself. Being a mum can be a lonely place sometimes. It might be the case that tomorrow you meet another mum or friend and not feel like that anymore, but we always hit that place when we look around us, and it feels terribly lonely and isolated.
It's easy to give advice on the lines of trying to put yourself out there more, but even that can be tiring and not rewarding a lot of the time. We need people on the same wavelength as us, people who get us, who give us comfort, not just people around us. And that's really hard to find when you have children and they come first. Our energy levels, what we can give in terms of time and mental space is very restricted when you are a parent. More so when you are single parent.
Take it easy on yourself, OP. Try not to put too much pressure on your social life. Just enjoy being in your own company for a bit, having a cup of tea, baking a cake, reading a book, watching a film. Try to give yourself for a moment that comfort and company that you might need from others. Somebody will come at some point and give you that, but in the meantime, try to give that little gesture of love to yourself, and don't think it's less worthy because it comes from you.
And post here too! Mumsnet is a great place to feel less lonely :)