Sorry you are having a hard time 💐
You know accidents do happen, you didn't do anything on purpose... It was an accident. Luckily your dc is OK, with no lasting damage. We all have accidents with our dc, some small some bigger, but nothing we wish or plan for, of course.
I think you a blaming yourself so much, because you are depressed already.
I have had cbt, my therapist talked a lot about automatic thoughts, when depressed they are generally negative. She suggested that every time I was conscious of a negative thought, to forgive myself for thinking it, tell myself it doesn't do me any good, and tell myself I choose to think of something positive.
I won't lie it is hard work, you have no idea how many negative thoughts you have until you work with them. But until you can get cbt perhaps try thinking positive as best you can. (I realized when I was in a bad place that smiling big, changed my mood a tiny bit, I know it sounds weird, but I worked for me).
Best of luck and smiley hugs 😀.