Anxiety Support Group
Anxiety is a physical condition marked by intense and persistent feelings of distress, fear, angst or dread. General anxiety caused by routine day-to-day stresses usually passes quickly and is experienced by almost everyone at one time or another. However, such feelings that linger over time and are very difficult to cope with, and which lack a clear cause, may indicate...
I completely understand you, as I myself have Avoidant Personality Disorder, a form of social anxiety. I have kept it from a lot of people, except from those that really matter to me.
You have to weigh the pros and cons with every person you tell. Some will be sympathetic, others won't. If you feel your social anxiety is affecting your relationship with your boyfriend then you need to do something about it. Like Gramybear said if he's sympathetic he will understand you and support you. If he's not then it's a good time to get out because it's an indication of bad times ahead.
If you decide to tell him do so without any emotions involved and explain what it is in simple facts, such as "I suffer from social anxiety, which means that I can get nervous in crowded environments." You could instead say that you're very shy.
That's how I've done it in the past, depending on how knowledgeable people are about mental health. For the most part it's worked, with the exception of one former friend who decided I was crazy and stopped talking to me. Her loss, not mine :)
Other people here I'm sure will give you more advice.
Take care
I wish you peace on your warrior's journey.