Little this is quite a common situation. I had no friends for several years. The clicky mums at playgroup were impossible to break into. Plus they were constantly out drinking and socialising and spending money like it was water - I simply can't afford that. They can't undertsand my life, much like most of the people at work can't.
But I agree with the other poster who said you do need to drop the 'friend's' who are pulling you back. Honestly stop. It is so liberating when you finally ditch them and realise well it's just me and I'm fine thanks and better in fact because of not waiting for them and being depressed and upset when they let me down again and again and again...
They are dragging you down and eating your self confidence. When I ditched my one sided friendships it was tough and scarey, but I am so much better off emotionally. And it has freed me up to find other friends.
It has taken a long time, I can tell you. Especially when you have to say no to evening stuff through lack of babysitter and money. I find it hard at work saying yes to the xmas party even. No-one understands what it's like having no fancy clothes, no money for petrol there and back, no babysitter....
I finally made some friends through school, though again not good friends but it'a a start. Again seemed to be me doing most of the running about and mostly so my ds could have friend's after school etc. And then the PTA gave me an outlet. People to chat with, things to fill time with, make myself useful without it costing me too much other than time when ds could be there too.
So I made some 'friends' through that, though again not good friends, more what you would call acquaintences. But it's a start.
And I now have one person who I can ask for a favour sometimes, another friend who will have my ds to sleepover (though I have to reciprocate by having both her ds's over), and my neighbour (who's dd spends most of her time round here) I could occassionally ask to help with school pick up if I was running late from work. (Though her partner doesn't like other kids in the house when he gets home from work so not for long). Plus again very one sided as her dd practically lives her yet ds rarely goes there. At least he gets some company though.
Do make yourself go to places, even if it's just to the park, soft play, coffee mornings etc. And take a book with you incase you do find yourself feeling like billy no mates. And when your dc is old enough sign them up for scouts (or whatever) to get yourself a little bit of you time. PLus you can offer to help out on the rota like I did and meet more people that way.
Oh and it's not just us lone parents that get cancelled on and forgotten. I forced myself to go to Jamie Oliver party I was invited too. More than half the people invited forgot or canceled at the last minute. Felt bad for the host, and felt more sick at the prices they were asking for stuff! Fortunatley I had to leave early to get ds from scouts. Still ended up getting an unwanted xmas present at a hugely inflated price. I don't know how people can have that kind of money to waste. £14 for 4 wooden spoons!? I digress..
And I was invited to a NY eve party at my sisters a few years ago, but a (now ex) mate wanted me at her party too. Felt torn and unable to say no to either given I rarely get invited at all. So went to my sister's saying I could only stay a while. She was desperately trying to make me stay as only 1 other couple turned up.
Also note I have now stopped running round after my sister helping her with her child care, taking her children on loads of days out, swapping my hours at work to help her with child care etc (she is married btw) while getting almost no support from her and almost having to beg her to have ds on the few occassions I have asked as I have to work on the weekend. She would happily say no, I found it impossible. But now I've said no it's so liberating. All that weight of expextation to reciprocate, help because I'm on my own and to include my ds as he has no other family has now gone and I no longer drive myself crazy wondering why or what I did to end up with so little help and support.
So drop those useless people in your life and move on. Stop worrying about finding love and instead concentrate on finding yourself and making a life for you and youd dc until you can afford (emotionally and economically to do otherwise).