This is what happens when you are identified with your work to some degree. The work becomes you, hence criticism appears to be no longer about your work but your person.

My experience is that this often happens to individuals who have a perfectionist tendency. A very admirable trait that unfortunately can backfire in the form you described.

I think you already made the first step, which is becoming conscious of this. In my experience, the second and harder step is to stay conscious.

For me personally, it helps to take a step back and get some distance from work (even if it is very short).

Also, what greatly helps is not condemning yourself for your reaction to that criticism as that would just add one more layer of negative feelings on top of it.

The reason you react this way shows some very positive traits in you. Appreciate them.