I don't think they're supposed to solve what's wrong with you when making a question about your well-being; as you say it yourself, it's up to you, not to others. People can try to help and alleviate the pain but it won't be an ultimate solution after all
Being honest about not being ok really depends on who you're talking to however, some people will show genuine interest and care towards you and genuinely try to make you feel better, while others... Simply ask because it's the normal thing to do, it just comes down to yourself and who you feel like opening up to, I personally don't think it's a bad thing to keep it to ourselves as I personally don't want to overwhelm anyone close to me, I know they got their own issues to deal with so..