If the student is ESE there should already be accommodations in place especially when it comes to testing. Looking at the student IEP plan or talking with other teachers who may have the student would help you get a better understanding of what accommodations they need.

Some form of alternative assessment might be helpful to keep this student from being stressed. Maybe testing the student orally would help to relieve stress?

I would look over the students IEP or 504 plan. Many ESE students are brilliant but have problems with issues such as anxiety when they are more than capable with dealing with the tasks presented to them.

I would try testing them differently and looking at their accommodations to make sure you are doing all that you can for them.

You should always do accommodations specially when they are taking a test. Looking at their IEP is also very helpful to have knowledge of what you can do to help the student. Have communication with the ESE teacher is also important because she or he can also help you.

I believe accommodations should be made for him so he doesn't get stressed and nervous.

If the student is only having difficulty in social situations, I would suggest some possible interventions. Perhaps set up a system where the student is given a sign that he'll be asked a question soon so he is not surprised. Another might be to avoid asking him questions during class altogether. While not ideal, you could look at his paper throughout the lesson to determine if he is grasping the material.