I counseled opiate dependent people before I began applying to MSWs, but I was a bus driver with a degree in History before that and had absolutely no experience in social work. I have always had mild social anxiety, but I also have a rather weak constitution and usually did't tell people (especially co-workers) how uncomfortable I may feel in most counseling situations. In the beginning, it was very scary and I was just freaking awful at the counseling part of my job. After a while, I was turned on to the techniques of motivational interviewing and reflective listening (look 'em up). This really took the pressure off me and placed the onus on my client to, more or less, reach their own conclusions by pitching their thoughts and concerns against me, and I would simply pitch it back with a twist of cognitive dissonance, affirmation, or understanding.
Counselors aren't expected to give advice, but simply be present and give people a chance to work things out in a safe space with a compassionate person. Increasing confidence helps, but this is a hard process that only comes through trial and error and is pretty painful. However, the fruits of experience are very rewarding.
Embrace your training, gather advice from those with more experience, and accept that you're going to suck in the beginning of everything you try, knowing that you have the intelligence (as evidenced by you being in grad school. 'tis no fluke) and the knowledge to eventually become a competent social worker,
Most of my friends have anxiety and I worked with a lot of clients with it, too. Like the above poster stated, it becomes a self perpetuating thing unless you seek counseling, learn skills to cope with your anxiety, or accept that you're human and work environments put us all on the spot, which is part of being in the world, I guess.
Next time you feel anxious and are removed from the social situation, look back, step outside of yourself, and ask "what in that moment made Jolcia17 uncomfortable? Why was she upset by this? What does this say about her? (beyond that she has social anxiety because she already knows that) How can she hope to have a different outcome in the future? What needs to happen for that to be a reality"
Peace