Hello xxAmyxx!

Well - I think some clarity is needed and seperating things out. I will explain:
You talk about you shutting down - this in itself and issue.
I think the fact that he reacts to that with anger - is another issue
Then there is the dynamincs between the two of you
Then there is your past (abuse that you carry with you and imapcts your behaviour
And there is the fear to trust
You also mentioned that he wont tell you what makes him upset - so the communication between the two of you as well as both of your emotional intelligence is lacking.
For all these - I really really think you would benefit from seeing a counsellor / therapist together.
You know that your response (shutting down) is not helping. His anger at the situation probably escelates things. So you have to learn why you both respond the way you do, how to change it and new ways of responding. This is hardly impossible to do alone for a sustainable amount of time.
My guess is that the not speaking not moving response is a learnt response. Something you did quite early on in your life and never really learnt healthy ways of dealing with conflict. This response is not helping your relationship - you know that. Talking, sharring and trusting your partner to work on things with you while exposing yourself and how you feel, what makes you happy, sad and angery (yes angry..) - is the only way to grow as a couple and be strong together. If you were abused in the past - of course you will have difficulties doing that. Why would you want to make yourself vulnerable... The risk is too high - you may get hurt and you are probably not sure what will happen next.
To start with - I would explain to the BF in a moment when things are fine and calm that you have an issue. That you know that your response is not helping the relationship and that you know how frustrated he gets. Then I would explain that I do not do this on purpose and that I cannot help it and need help to change. What do you think he woud say to counselling?
I hope this helps dear!! x
P.S. I used to respond like this and I promise you - it can change if you want it to!!