The two suggestions mentioned seem to only kind of 'tone down the volume' in a way, (not important enough to be concerned, people aren't thinking about you) which does not address the root of the issue of being attached or kind of enmeshed, be it your parents or whoever.
Lets just put it in plain language: you want to be liked, and you are afraid of not being liked. None of that actually deals with who you are, which at some point may become a conflict with the conditions of being liked 'set' by others, whether consciously or unconsciously. Ideally, of course, at some point you know yourself pretty well, and as far as what other people think or feel about you, you are also at peace with that - but you do not try to pretend to be someone you're not for the sake of being liked by others.
There is being free from something and being free to something. When you have a (seemingly) big hangup like wanting to be liked by people, maybe certain specific people, then the concern naturally revolves around being free from that. In general this is where people start focusing on, and the way to do that is to simply question it - is it true? (if you program yourself with affirmations to the opposite effect, it would be more of a competing thought) More importantly, it helps to make a distinction between that tendancy to wanting others to like you and YOU, who you are, and when you recognize it's just a tendancy maybe extending from childhood or whatever, (which doesn't have to be a big psychological drama, after all it's quite natural and prevalent) then it doesn't seem like such a powerful thing - you have become conscious of that behavior.
But here I want to emphasize the very subtle behavior of turning that recognition into a concept and not going deeply into it all the way. You can say "oh yes, I see how my relationship with my parents contributed to this" or whatever, but having that thought in the head isn't in itself going to free the whole mind. In other words, there's no substitute for a complete realization of how your consciousness is as a whole, and seeing past that framework. We may have a thought like that after we've actually gotten some perspective and see ourselves and where we're at, but that thought is actually an after effect. It may start with a specific inquiry, but for this to happen thoroughly it has to open up to include your whole mind, which is a kind of relaxing, taking in the big picture you might say. To put it another way, to shift your consciousness you don't work at it in a piecemeal manner, but you see the whole and the whole thing shifts.