Well I suppose the reality is that if you can’t be happy, if you have tried, and you can’t then that’s kind of that.
But for what it’s worth I think you have it a bit wrong. There will always be suffering. And inequality. And injustice. It doesn’t mean, in my view that you should not seek and find joy where you can.
I have always been engaged in politics (national and international). I used to be an active member of the Labour Party, did a socially useful job and volunteered throughout my life from teenage years onwards (a few different roles, but the most long standing were adult literacy, visiting older isolated people, and then the Samaritans). I never felt that my volunteering made me a “good” person. And I didn’t think it cancelled out the suffering I encountered. But I did make a small difference to the lives of the people I encountered. Alongside my awareness of how much suffering there was, I was also able to take real joy in the life I had created with my husband and our 3 children. We had a blast. I don’t think that made me an uncaring person.
Then in October last year my darling oldest daughter died, entirely unexpectedly, aged 24. My daughter was one of the most joyful people I have ever known. She bubbled over with laughter and kindness. She was hugely empathetic but also really enjoyed life. I shall never get over the loss of her. It’s her birthday in 2 days. The despair I feel is absolute. But I’m glad I took the joy when I did. And despite my pain now, I do not begrudge others their happiness either. My close friends are moving on with their lives now, still supporting me, but taking joy where they can. I want that for them.
It sounds trite I know and I don’t mean to lecture you OP, but I would say just make the most of the life you have, enjoy things as much as you can. And it is possible to combine having fun with doing some good, bringing some comfort, adding some joy along the way. Making the most of the life you have does not, in my view, equate with not caring about others.