Anxiety, just like every other thing, can be improved if we work on it. I am and I always was an introvert. Overall I don't know if I've gotten any better, but I haven't gotten any worse either. My work situation during transition really helped in normalizing the situation though and I can easily imagine having developed some social anxiety if it hadn't been for it. Being an introvert is not a problem though. I quiet like being one as it gives me time to observe and think.
There is one piece of advice I rarely hear mentioned though. As with social anxiety most of us have some thing or some habit that we can or should work on. But self improvement is hard because we are creatures of habit and it is easier to leave things the way they are. When we transition however we have a tremendous amount of energy and motivation. This is an excellent opportunity to let some of that excess energy spill over into other areas of our lives that could use some improvement as we are already pushing ourselves through uncomfortable territory. Transition is really about self improvement so make what other issues you may have part of the package. When I started my transition I barely had an income and was up to my neck in unpaid bills and a defaulting student loan, but I worked really really hard and by the time I was all finished had been made manager at my workplace and all my financial skeletons had been cleared out.