It is not right that she forces you into uncomfortable situations. Since you are chatty with friends it may that your mother is correct that you need more life experiences in order to gain the confidence to deal with other people, however her method might cause your problem to get worse. Is there a counselor in your school that you can talk to?
It does sound like you have an anxiety problem and it's getting worse. Your mother actually has the right idea but the wrong way of putting it forward -- the more you face your fears the more likely you'll stop being afraid. But the better way to do it, given how you're describing it, is to see a psychologist who specializes in anxiety treatment so you can get an understanding of what's going on and learn some techniques to help you relax so you have some tools in your tool kit to use when you confront your fears. If you stop thinking anxious thoughts, this will go away, but you don't just say it and it happens, it takes some help and understanding of what's going on. Talk to your mum about it, and if necessary, show her this forum to help her get that this isn't so easy. As for the term social anxiety, it's used for convenience, but anxiety can attach to lots of things. The problem is anxious thinking, and, as you already know so you're already ahead of the game here, the thinking isn't rational.