Sorry to hear you are going through a rough time, thanks for reaching out on the forums.
Its good to hear that you are willing to change the situation, just perhaps you don't know where to start? I can relate to that. Your post jumped out at me, because I have had some trust issues in the past as well. In my opinion, it is something that can definitely become better and be worked on.
It is 100% understandable that you are having issues, moving and friendship troubles in the past are things that impact trust quite a bit. You are very resilient for going through that disruption to your social support and still be willing to try and reach out. Kudos to you.
For making friends, at least at the very start, you need to spend consistent time together with someone. So, for example, meeting them once a week for a few hours. If this doesn't happen in some shape or form, I've found (personally) that the friendship gets hard to keep up. Chatting online can be time spent together as well.
You say you have been to events, and that's an awesome way to go out and meet people. I'm just wondering if you may have had trouble because the events weren't consistent & often enough, or with the same group of people? (I have no idea, I am just throwing ideas at you just in case)
When it comes to trust, it can take time to break that barrier. What worked for me (again, just personally) was making a friendship with someone first, and then getting closer emotionally. Surface-level friendships can definitely be made without spilling your heart open. Especially if you have some kind of common interest. Once I knew that person was a genuinely good person, and was opening up to me, I could do the same as well. It may feel uncomfortable at first, still, the right kind of person is patient and won't rush you too much. Please be patient with yourself and take as much time as you need.
Opening your heart up to friends is like any new activity or habit. At first its a bit awkward and uncomfortable, you may not know what to say. Over time, you may become more comfortable with the other person and trust forms. As time goes on, you may begin to seek that person to talk to, because you trust them.
Trust is this big long journey sometimes, and its okay to be at the start of it. It doesn't mean you won't reach the end. I hope telling my story helps you. You can get there, 100%!
Last, researching Attachment Theory might help you.. the test gives some interesting information.