That sounds like an anxiety response. As you said, your brain just isn't listening. The first step is recognizing what is going on - the questions have set off your anxiety and broken your ability to answer questions.
So you have two choices, if this is a live presentation:
1) Get back to a healthy place right there, quickly. There are a variety of techniques for this which will take some practice. It can be as simple as taking some deep breaths. Or more complex, such as reminding yourself that their questions are not attacks, and answering them can open dialogue that takes you all to a better product.
2) Decide that you have hit your limit, and gracefully end that part of the presentation. I recommend honesty in these cases. Say that you did not expect the questions, and you would love to answer them, but are feeling that the pressure of the surprise questions is throwing off your ability to answer them well at that moment. Ask for everyone to allow you to finish the presentation, and send questions to you, which you will answer when you have some space to put in the proper effort to writing up the answers.
If this is not live, and instead is async written communications, you are free to step away for a time and come back to it when you are ready.
I honestly recommend a brief stint in therapy to learn some CBT skills. This is exactly what they are meant for - to help you identify when anxiety or other problems are stopping you from succeeding in your daily life, and give you tools to work with in those situations. You can learn these skills fairly quickly in a few therapy sessions, so it really is more like a few weeks of training, not formal "therapy".