Well... I don't know how common it is to think about self-injury. I think about it pretty-much all the time.
(I also have a lot of passive suicidal thoughts.) I've never cut. But I have permanent problems related to self-harming I done in the past.
Should you be concerned? Yes, my personal, non-professional opinion would be you should be concerned. I don't think you should be
scared… but certainly to be
concerned would be appropriate I would think.
Something is driving this spate of self-injurious thinking. And, at least based on my own experiences, this sort of thing has a way of wearing you down over time.
So my thinking would be that it might be best to talk all of this through with someone in real life if that is a possibility for you.