In order to relax under difficult encounters you need to physically train yourself not to react in the fight or flight mode.
You’ve acknowledged that you are probably experiencing an Amygdala hijack. That’s a great first step. It means you recognize the problem and are willing to do something about it. You realize that the challenge is to not to react like that in the first place.
An Amygdala hijack is a body’s way of dealing with fear and threats. If you were truly in danger, say for example if your house was on fire, then fear and fight or flight reaction is the appropriate response.
In a social situation however your life is not in danger. Your imagination visualizes what could go wrong and this generates anxiety. Biologically anxiety creates the same physical response as fear. In this condition your instinct is to protect yourself. You want to either run away or hide and make yourself invisible. Or you snap back pre-emptively offer up a cynical or aggressive comment. That is not connecting, that is protecting.
Because anxiety is a construct of your own mind, you can learn to respond positively by getting used to social encounters. Take a deep breath and acknowledge the fact that what you created you can undo. Practice the items below and you will learn to react more positively in social situations.
Your goal is to connect with other people with comfort and ease.
Before getting into how you can practice I want to say that this is not about putting other people’s needs before yours or that your needs come before others. Imbalances of ego, I believe is how most situations become sticky in the first place. Emotional stability is requisite to becoming a mature and connected adult.
So for the sake of this question, let’s just assume that everyone’s needs are equally important.
Instead of hiding or avoiding situations that affect you, go to where the action is happening.
Offer to lend a helping hand or a helping comment. Look people in the eye letting them know you understand and you are there if they need you.
Be willing to put yourself out there even at the risk of ridicule. It does take courage and it is certainly not the most comfortable route. But you can't be a person with soft skills if you aren't willing to take the risk of putting yourself in "harm’s way". So practice just walking over and make yourself present even if there is no action taken. It might sound like a strange thing to do but if your instinct is to be present rather than becoming invisible, you’ll go a long way towards connecting with others. Take it one step at a time.
Put the focus on other people. In a way this makes things easier. You don't have to worry about explaining or defending yourself. Instead be concerned with other people.
Feel the empathy, walk a mile in their shoes. What can you do to make this a better place in the world? If you see someone having a difficult time, walk over and ask "what can we do to make it right?"
Just asking shows not only that you care but that you at least understand that a vision exists on how things ought to be. This is leadership.
You’ve shown up, seen things from another's point of view. Now is time to communicate. Be open. Share. This is where you make yourself vulnerable. Asking implies you don't have all the answers. Whatever you do or say it might be the wrong thing. It’s ok. You can course correct. If your heart is in in the right place people will understand.
A good way to practice engagement is to ask questions. Listen and ask more questions based on what you heard. In time you can offer up your best answers but asking and being curious is what shows true engagement.
Nothing is worse than a snide, cynical response to an attempt at openness. Of course you won’t offer this. You will be agreeable because you are coming from a strong place.
Empathy will let you see that other also experience an amygdala hijacks. You do need to be internally strong for this. You cannot be agreeable simply because your ego is weak and you want to please. To practice this you need to be aware of your own responses to others. This means you have to actually make those connections. Show up, be conscientious, engage and respond with kindness from a position of strength.
It’s tempting to think that some are born extroverts and others are not, but the reality is that the extroverts probably just had more opportunity to practice throughout their lives.
I do recommend a few books in these areas. "Linchpin" by Seth Godin, "Daring Greatly" by Berne Brown, "Finding Inner Courage" By Mark Nepo, and "The Chrisma Myth" By Olivia Fox Cabane