+1 to Jeep - lots of good ideas there.
It's so much easier to deal with someone else's problems isn't it? I totally understand that. That gnawing feeling of worthlessness can really engulf us. But it is just a notion, we don't have to listen to it, or accept it. It will pass, and you are worth so much to so many people.
One of the ways I have found I can sometimes get round it is by talking to myself!! I know that sounds daft, but I talk to myself as though I was someone else (I'm not sure that would be a good thing long term but it helps in the moment!) I just say stuff gently but firmly. Like "okay, so why not make a cup of tea? That's always nice. Just pop in the kitchen and boil the kettle..." and so on, literally talking myself through what I'm doing, almost as though I'm teaching someone to do it. Sometimes I carry on through the details, and point stuff out like "look at the swirly patterns in the steam" and I say lots of positive praise things, "that's it, well done" "good girl" etc. That way I can do something that distracts from the thoughts of harming and the general negativity that can otherwise have me superglued to the sofa. I usually find that once I can start to do something, and get a cup of tea or something in me then I can get some more positive momentum.
That may sound completely batty, and might not be useful for you, but if nothing else, it's made me laugh reading it back
Keep talking, you can get through this xx