As an introvert, (INTP who occasionally scores INFP on the Myers-Briggs test) I can attest to the difference between shyness and introversion. Introverts process feelings, experiences, and ideas internally, are highly introspective, and do not generally need to outwardly express themselves through interaction with others. Introversion does not equal insecurity. Many introverts are quite stable and confident and are not needy in the way that many extroverts can be with regards to other people.
However, with the realization that in virtually any career, an introvert will be required to interface with other people at some point, it is a good idea to hone one's social and speaking skills. I can speak to this through personal experience. As one who is often quite content being alone in my own mind, my social and speaking skills diminish by virtue of inactivity. However, through deliberate effort and practice, I can polish my skills and no one would be any wiser that I'm not naturally inclined to be social or a good speaker. That's why I suggest, OP, that you do join organizations designed to enhance these skills, because I suspected from your post that you do not feel confident or comfortable in these areas.
Seriously, check out Toastmasters in your city. It would be different attending a community Toastmasters meeting rather than a university sponsored organization simply because a wider variety of membership would be represented other than college students. It would also be full of people like you who are also not confident in their speaking skills and are seeking to improve in a supportive learning environment. Not only do you practice public speaking, but there are also activities designed to enhance your interpersonal communication skills, either one-on-one or small group settings.
I think you have the capacity to do just fine in law. In addition, you are mature enough to recognize and admit your weaknesses. While working your strengths, you can improve in the areas in which you doubt yourself and be an indomitable force in whatever you choose to pursue. Good luck!