My speculation and suggestion:
ATM you are (or, might be) on the edge of some useful humility regarding those emotions. If you try to avoid them then you will never master them. If you want to be unaffected by them (and remain rational in spite of them), then you need to master those emotions.
If you want to respond positively to criticism, then this is a chance to practice that. You say that you’re “afraid”. Is that not an instance of being afraid of criticism? Those moments (when you do get emotional) are the best chance for you to figure out why you have those feelings and to understand them - IMO. It’s hard to introspect about something the further in the past it gets.
Here is my suggestion: read https://fallibleideas.com/emotions
The final section is “How To Change Emotions” – you should read the entire article, slowly and carefully. (and post about stuff you don’t fully understand and your ideas, too – that way ppl can help if you get stuck on something.)
One thing I have to add to the article that helps me: in those moments when you slow down, consider your goals – what are you actually after; and consider the other person’s goals, too.
Edit: IDK if this post is okay for this category. I posted about that here