Thank you for your post and your question. I think it is a big vague so I'm not really sure how to answer it - maybe if you give us some examples it will help! But in the meantime -
Part of self care is intentionally thinking about your own needs, yes - but probably in the sense of thinking about if your own needs are met - like self care could be having a nap when you're tired, or sitting with a hot chocolate because you're cold, or deciding to read instead of work because you need a break. So when thinking about self-care, there's probably a bit of curiosity there - what do I need right now? Are my needs met?
Your second question, which feels quite different to me though is more about anxiety.
Trying to ignore your fears to me seems like trying not to think of a pink elephant. It's there, and the more you try and avoid them the more that you'll think about and have it consume you <- This is what health anxiety looks like. What we can do though is acknowledge those fears without necessarily acting on all of them. As an example, someone with health anxiety might see a rash and immediately go to Google it, or immediately go and see a doctor. Someone without health anxiety might see a rash and still have those worries, but decide to 'wait and watch', deciding to see a doctor if it's been a while and it's still there. Someone who is complacent might see a rash, ignore it completely and not see a doctor at all.
Hope this helps in some way?! If I'm on the wrong track maybe you can give me a little more clarity