I've spent my entire career battling the type A vs type B personality dilemma since I am in the latter category. Not exactly social anxiety, but a near cousin in that it is very difficult to talk to folks and especially hard to sell yourself in an interview. Unfortunately many hiring managers seem more impressed with the type A individuals because they are the salesmen and tend to be more aggressive than type B which is actually a job requirement for them. As a result, the type B folks tend to get overlooked. It is not discrimination but rather the nature of some jobs. The key is to build up a story about yourself and your accomplishments that can be included in your resume. Let your resume and cover letter speak for you. Give facts with specific examples of your accomplishments, awards, etc which will demonstrate your talents. Focus on your ability to write, learn, research, use software, etc. Anything you see as your strengths. There are tons of jobs out there that a type B personality can do and utilize their strengths without having to face clients, customers or even a lot of other teammates. The trick is realizing that all type A people NEED the type B folks in order to succeed.
I am not sure about current practices, but when I applied for College (and later when my kids did), the screening was done based on your grades, SAT/ACT scores and an essay explaining your desires for the future. I would suggest using your time between now and graduation, looking for opportunities like Dana suggests in an earlier answer so that you have good material to work with when it comes time to write your essay. This is also the foundation and something you can build on when it is time to create your resume. Focus on what you CAN do and don't worry about your weaknesses. Most employers that are actually looking for type B people, are not concerned that you have the weakness, just that you recognize it and are either working on it or at least not letting it cripple you by focusing it too much. You are already demonstrating initiative by asking this question. Look for other examples where you have taken the initiative and document them. It is great material.
I actually started my College career with a totally different degree plan than I ended it with. I started working in a field which is totally different from what I am doing today. Always do your best, be willing to fail (since we all do), learn from your mistakes and you can be successful. I would love to be a Vet and actually got my degree in Animal Science. Now I work from home for a High tech company. Opportunity presents itself in all forms. Watch for your's. Good Luck!