It's like you wrote this post right out of my life...
It's a struggle and trust is a big part of it. I've found that focusing on my intent and my desired outcome with this kinda stuff helps me get out of my thoughts and emotions about it.
E.g., I had the opportunity to meet up with a girl I work with at a noisy public place. She told me it would be fun and all I could think of was, ugh that sounds horrible, how am I going to do this, Why did I tell her yes, etc. And i honestly didn't want to go at ALL. But I knew if I kept dreading it and staying with that attitude I'd end up blowing her off and not going. I knew I needed to go just to try to branch out a bit. So I kept at myself, I kept telling myself "you need friends", "you've never been there, you don't know enough to have an opinion yet". Then I told myself what I wanted, "I want a friend ", "I don't want to blow her off", "I want to thank her for her invite by showing up", "I would hate to insult her by being flakey after i agreed to go". I went and yeah, there were some uncomfortable times but I'm happy I went. I'm happy I challenged myself to do something really uncomfortable for me. I feel better able to do something like this again in the future. And I know the more I do things like this, the easier it will become and I may even one day learn to enjoy myself.
As far as the 'cold responses', somewhere inside you're just trying to keep a safe distance from people. It's okay not to want to jump right out there and welcome everyone into your life, even when you're desperately lonely. Can you find one or two people you trust enough to not take your responses too personally, and maybe take some small steps toward building some familiarity with them? Maybe mentioning a favorite movie or restaurant or show, asking them casual questions to show you're interested in getting to know a little about them. Maybe practice smiling some when you speak, even when just saying "yeah", or just smiling at people when you make eye contact or say hello. Practice this because when I started doing those things I wasn't used to it and yeah... lol.
I see hope in that at the very least, there's a desire in you to change yourself and your life, and there's plenty of room to grow. You can do it. Practice makes perfect. Baby steps and encourage yourself. Celebrate small victories and forgive yourself when you can't manage bravery some days or if you embarrass yourself... just keep trying. You WILL get there.