My little Izzy is hurt

I was just giving her some food and water and she was running around me and leapt up onto my lap, I stroked her but noticed pink on her back (she is a lionhead so has lots of fur/hair?). When I looked closer there were cuts and scratches along her spine and the skin looked quite sore around them and clumps of hair missing

... I'm unsure of wether a cat's got to her or not (she is only tiny at the moment). Anyway, I boiled some water and let it cool so it wasn't too hot and bathed her cuts just to get any possible dirt away, they look quite clean. I've just got to keep an eye on them for a while, see if they heal ok and don't get infected or anything. She's eating and drinking properly and still playing so they can't be bothering her too much. I think I'm probably more upset than she is, my poor little Izzy!
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Makes me that much stronger
Makes me work a little bit harder
Makes me that much wiser
So thanks for making me a fighter