Complaint about me and now spiraling

I had an informal complaint made about me at work. I’m devastated. I know I can get grumpy when I’m under pressure and when I think the processes that I have to do are stupid, but I never intend for that to come over as being aggressive to the person I’m emailing. I’ve apologized (making sure I’m taking responsibility, not just saying “I’m sorry you feel this way”) and I know that that will be it resolved as far as work is concerned.

I just hate thinking that they’re upset (I know that’s because of their thoughts, but still) and I’m really struggling not to spiral into “everyone hates me,” “why couldn’t I have done this differently,” “this is all because you got behind and put yourself under pressure, it’s your fault,” and even “how can you want to be a coach when you can’t even do this right.”

I then add an extra layer of guilt because I don’t want to be the person who gets upset/attention etc when I was the one in the wrong (I hate it when I see bullies etc go “oh but you’ve upset me by calling me that” and I don’t want to be that person). Not really sure where to start with self coaching or whether to just feel the feels today and work on the coaching tomorrow.