I am in 2 minds here, as I think if someone has a baby, that is their choice, and their responsibility, and they should not expect people to look after them whilst they go out partying/to concerts etc. And when mine were little we had no support (for a number of reasons including we both had very small families who lived far away, or just couldn't help for various reasons....) and we were 100% responsible for the childcare of our 2, and if we DID need or want to go out alone, we had to pay babysitters. We also had to pay a childminder when I went back to work.
Then again, I think it's nice if family CAN help, and CAN show support to younger members of the family who have young kiddies. And to be honest, I saw a number of people leave their kids at their parents for 3 day weekends whilst they went partying or went away for a weekend, and we had no-one, and it made me a bit bitter and envious at the time. (I did have/do have several cousins but would not leave a hamster in their care to be honest!)
So yeah YANBU OP, and I hope you manage to find some help and support soon. Maybe join a hobby group/parents group, and try and join or form some kind of network.
All I will say is even though I was a bit bitter and envious, (of all the people I knew who left their kids with other people whilst they went out a lot,) is that me and DH are incredibly close to our 2 kids (now in their 20's.) Basically, it was, for the most part, just the four of us, and we are like soulmates, and have a fantastic relationship with them. The parents who we knew who got others to look after their their kids a lot (whilst they went out socialising,) are not particularly close to their children now.
Not saying people who left their kids with others while they went out socialising, will have a bad relationship with their kids when they're older, just that IME, the children who went to stay with family, (very often,) whilst their parents went out socialising, are not so close to their parents, as we are to ours. We have a very strong bond.
If I were you, I would try and make a few new friends (as I said before,) but also get a paid sitter so you don't HAVE to to depend on family. Some of those people I knew who got family to look after their kids while they went out socialising, took the piss out of them, and it was very unfair. (Not saying this is you by the way. And good luck.) 
Also want to add that there is nothing WRONG with kids staying with family whilst the parents go out socialising, but if it's all the time, it's not fair on the family looking after them all the time...