To be honest, being a new parent is really hard and I think everyone has these feelings of loneliness at times - I am not trying to minimise, more to say that you're not weird or anything!
When I became a parent, I found it really hard because none of my friends had children yet and the mums I did meet were all older than me. I wasn't a teenage mum or anything - I was 24 when I had DD1 - but often they'd say things like, "Oh, bless her, she's such a baby!" about me, which kind of didn't lead to a natural equal friendship vibe.
I'd say two things, and they're linked. Firstly, maybe expect less from the friendships. These are just women who've had a baby at roundabout the same time you did. They're not necessarily soulmates. You might not even want them to be! They're people you can be friendly with and build a friendship with perhaps, but they're not automatically potential super close friends.
Secondly, if you can get into that mindset, it might actually help you with making connections. Often, when we're just really eager to make a friend, it inhibits how we interact with people. We become too "nice", too eager to please, and it doesn't come across as very natural. While it's not a bad thing to be trying to be pleasant, it might make it harder for others to get a sense of the real you.
I don't know if this all sounds horribly wishy-washy, but if it helps at all, I'm glad it does. You will find people, I promise! But there's sometimes strength in just being, and waiting for those connections to happen rather than forcing them.