Reading your post and​ going from my own experience of (Social) anxiety. I think perhaps a therapist would be of more help then going straight to a psychiatrist. From experience psychiatrist tend to be more for prescribing medication which isn't always effective and if your main concern is anxiety will only treat the symptoms rather then the root cause. Medication and therapy in conjunction could be and in my case was more help. Therapy will help you to understand whats causing your anxiety and look at ways to cope with it, whereas the medication just masks the symptoms. Perhaps look into a therapist whose trained in CBT (Cognitive behavioural therapy).
Good luck​.