Slow down. Take a deep breath. There is nothing wrong with you. You are a beautiful person and just because you feel like there are no close friends to you right now does not mean that it will be this way forever. I am so glad that you keep yourself busy and active, I bet you have people you enjoy spending time with and that enjoy spending time with you, but that you or they just haven't made those steps to meet up outside of those settings in ways that both of you are comfortable with. Lets just take this one step at a time. Lets set a goal - something small, something achievable. What do you want to see change in the next few weeks to make things better - yourself or your surroundings. Then ask yourself what choices would you need to make to help you move in that direction. No one deserves to feel lonely.

There is nothing wrong with you, quite to the contrary in fact.

You say you are a good listener, that's good, become better at it even still, and how? When involved in conversation only ever make it about you if invited to, and be as brief as possible turn it back to the other as soon as you can, it's always about them and never about you. Avoid me2 convo's, because in such type interactions there has to be a winner and a loser, your opponent never wants to lose, so let them win, letting them win means you win too.

You are a carer, enhance such fine quality.

Once again I can't figure out the answer or solution to another one of life's problem. I just don't know. But what I'm inclined to say is that I've gotten quite used to not being socially attractive, which is what I call it when people literally do not want to be around you if they can help it but oblige whenever they can out of courtesy respect and pity. I think it's all really charming to be honest. And sometimes I think, if only they knew the real me, they'd probably sprint lol. I think you'll figure your situation out on your own in time which may not at all be the same as mine. Just don't be too hard on yourself.

better to be alone than in bad company

Don't worry I feel exactly the same. I'm always the one trying to make friends. It seems like I feel left out most of the time. Do you have any hobbies to keep you busy ? Exercise is a good why to lift your mood and healthy eating. Are you introverted or extraverted ? I

I'm no expert but years ago, I found myself thinking the kinds of things you just wrote. It is so easy to think others aren't interested in you because you don't see the evidence. I believe there are more people holding back in gatherings, especially when they are not well acquainted with the other people than there are people who jump right in there. I don't like being the first to approach others either. Could you try to be a little more assertive? Or possibly could you just pick out a pleasant looking person who is standing alone to walk up to and speak. I think we all like to have the forward types around because they make it easier on those of us who are reluctant to be assertive. Anyway, I am trying to do more approaching instead of waiting to be approached.