I want to ask the op a question to understand things better, but lay some hypothetical foundation down first.
Let's imagine, if not true, that you now or one day have either a mother, father, brother, sister, friend or partner you care about that is very miserable and suffering--sad, angry, anxious, and/or overwhelmed by things unrelated to the hating advice topic--because of either their health, living situation, occupation they hate, or because of some intense pain, physical or mental, or because they feel too different, rejected, critiqued for who they are, rejected or alone.
Let's say that same distraught person was supported by at least one person much in the past, if not more persons in person or through some forum or writings, as there are obviously persons in life that like supporting more than giving advice, yet still that person continues to suffer, as seen by their own daily or regular words, actions and reactions, and as seen by others with empathy who may pick up on those things easily and may not assume what you are saying is actually best for you, as it defies logic.
Many people in life are wise enough to know support only goes so far, if it is assumed the other received support before and yet they have their recurring complaints or issues. Support is like a bandaid or temporary fix, and does not solve any recurring difficulties if you do not address those and get to the source. Many people instinctively give advice either because that is how they are able to show care, or as they subconsciously feel support is not enough, based on the complaints or irrationality seen.
Why is it you need support, and can handle no advice? Well, it is great you partially addressed this. You are a very sensitive person. But, it is unrealistic to expect others of different abilities, needs, desires, personalities and tolerances to do things only your sensitive needed way, or only tolerated way, as they may not have your same sensitivities, and as by that theory the others should be able to dictate too how they want things done too either because of genetics or conditioning..
So, the question is: if that person you cared about but was suffering greatly said to you often, after telling you of many of their problems, "I only want your support and no advice please!" would you just keep supporting them with no advice, like they wanted or said they needed, or would you start to get so stressed at them complaining and not getting to the source of those issues? An empathetic person could not stand their suffering and they themselves would need to do something more to stop their own anguish too. So, to be frank, and I do not care if anyone likes me here, I see it as sometimes strange for others to want support only, and no advice, and much of the support could be insincere anyway, or enabling. Any reply to you without harsh or unfair critiques shows often care, even if not the care you wanted. If you cannot see that most people giving advice shows care in their eyes, that may be the heart of the issue.
Do you know how much stress it is to hear person's complain all the time, and not want to even attempt to listen to sound advice or attempt that reasonable suggestion? Of course not all advice will help, but how will one know what things were attempted otherwise. And what takes more effort for most persons, one saying "I am sorry" or one racking their brain and giving many options to consider, or giving much information with the best of intentions? For any to argue the one saying "I am Sorry" shows more empathy is fiction, just as saying the one who gives reasonable advice against the wishes of the other must not be necessarily showing empathy.
Empathy can involve not assuming things, digging deeper through asking questions and giving advice, and in telling the other things they may not want to hear. Empathy can involve some support, and allowing others to be themselves yes, but if you have enough empathy too that requires you supporting others with different views and needs too, and allowing the advice giver to be somewhat themselves as well.
Just because others gives advice that does not mean you must follow it. In this society you will be dictated by many others in power, how to act and behave, or what you must do, and to abide by rules you may not agree to, so advice should be seen as less harsh than that. Advice is just an opinion, and often showing care of your current and future health and not any disrespect or poor judgment of you.. Opinions are how we learn too, and as we learn not just through facts.
I am not saying the HSP can get over any or many bigger things, but we cannot tell most society members to not step on our toes, and as they will often act in the way they see as best for you, if they care and want to assist, and if they do not know the extent of your issues and attempts to resolve those. They will not assume you know what is best for you if you are acting so troubled.
I am sorry for all your difficulties though, and I can see why it would frustrate you if you felt you could not change anything, but is it possible that one or more of your perceptions are different than reality? None of us are robots here. We all learn each day, have thoughts that can change some, and have tried new actions never done before. All of this can make us wiser and stronger. We all can grow some. Those who just support all the time everything, I sometimes see as enablers. Eventually, we all can learn to support ourselves with kind words if others do not support us anyway. That is easier I feel than coming up with all other solutions on our own.