first of all, thanks for being such an understanding mum. So many parents have trouble understanding what their child is going through when they develop a disorder like this and often dismiss it for shyness or a phase. But if it is SA, it usually doesn't get better without professional help (and lots of support). I am glad that you are concerned for your daughter, that's the first step to helping her with her problems.
When I first realized I had social anxiety and wanted to seek help I also confided in my mom. She brought me to our family doctor and he gave us a referral to a psychiatrist who I am still seeing. I recommend you to do this, as your family doctor will likely be able to refer you to a good psych in your area, and in the meantime he/she might even be able to start her on a treatment.
CBT is recommended for anxiety, but therapy alone is not good enough. Usually, the best treatment for people with anxiety disorders is anti-anxiety medication. There are several different types of meds available and they are generally very safe and effective, it's just a matter of finding the right one she needs, as some meds work for some people but not for others so she will likely be put on different types until she's on one that significantly improves her symptoms.
I think it would also be a good idea to have her make an account on this site or even just browse the forums here, as it can help a lot to see that she's not alone and there are many other people with similar troubles. It can also help for her to write about her problems and let out her frustrations while getting feedback and advice from people who are going through the same things and can empathize. SPW is a very accepting, supportive community and it can really help to have some extra support when you feel like there's no one else out there.