I’m glad the ice cube trick helps, because I’d much rather you do that than hurt yourself. <3 I am sorry that the negative thoughts are still there, though. :( If you’re having urges to self harm despite the anxiety being gone, I think it’s something that would be better to discuss with your therapist (if you have one. If not, self-reflection could help). It may be that the urges are still there because there’s something else going on that hasn’t been addressed yet, so it’s important to really assess what’s going on for you emotionally right now. But the urges could also just be out of habit, and I think that’s the sort of thing that will fade over time. So like I said, it’s something to think about/discuss with your therapist!
As far as whether or not the negative voices will ever be gone, I cannot make any promises - but I can say that I personally believe it is possible to get to that place. I think it takes a lot of time, a lot of hard work, and a lot of refusing to give into the urges when they come up now, but I really do believe with all my heart that it’s possible to fully recover. Maybe not to the point where the thoughts never ever come up again, but at least to the point where when they do come up, you can just acknowledge what they are and let them go without having any real desire to act on them. I also believe that getting there takes a lot more than just physically not cutting - it takes getting to the root of the problem, and facing the difficult beliefs, emotions or any other issues that led you to self harm in the first place. It takes truly learning to love and accept yourself the way you are, because you would never harm a person you love wholeheartedly. I haven’t reached that point yet myself, but I like to think that someday, I will. And I don’t doubt that it’s possible for you to get there, too. :)