Twenty years into my career and also being very introverted, I will say you are most likely in for a very hard road ahead. As others have said, your work will literally have to speak for you and, unless you are truly outstanding, even that might not be enough to ensure a smooth career. People value other people whom they have a relationship with, whether formed through professional contact, lunches, company events, etc. (Even being an introvert, you will too; humans are social animals.)
What I would suggest is:
-Learn mannerisms to indicate that you're friendly to people you don't know well without having to interact much. For example, wave or smile (and I mean a sincere smile) at people as you pass them in the hallway that you know.
-The people you work closely with are the people that you will get comfortable with and be able to interact with more easily. These few people will have to form the basis of your professional network to help you find career opportunities in the future. While you are, of course, naturally helpful and hardworking, you're also going to need to be helpful, hardworking, etc. in a way that they can see and will vouch for to others.
-Maintain your network. Take the effort to meet with former colleagues every once in a while or contact them on social media to see how they are doing.
-Force yourself to attend corporate parties and other events, as much as you can tolerate. You don't have to stay the whole time but at least be seen and remembered by your immediate co-workers.
-Get an understanding of how performance reviews are done at whichever employer you eventually work for and make sure that you are known in a positive light to the people making the decision. The extroverts do it naturally, you may have to do it artificially (cynical as that may sound). Failing to do so will hamper your career growth significantly.
-Having difficulty talking to others doesn't absolve you of the need to communicate. You're going to need to be able to need to write email, documentation, code comments, and so forth quickly, clearly, and concisely.
-If public speaking is a problem for you, work on that until you're able to give at least a passable engineering presentation. Engineering is a team sport and the more senior you are, the more you're expected to speak up and guide others. Organizations like Toastmasters and course like the Dale Carnegie program can help with this. The earlier in your career you confront this, the better.
-Seeing a medical professional may be helpful in ameliorating your introversion. However, be very wary of medications; they may come with nasty side effects including reducing mental acuity (a massive problem, if you're a technology professional), rebound effects, tolerance effects, and withdrawal effects. Therapy and modifying your behaviors are the most likely to succeed in the long run but require a lot of hard work on your part.
-Be prepared for pain and frustration. Bad ideas communicated well by someone else will win out over good ideas that someone is unable to communicate. Less talented people who have good relationships with the organization will succeed more than a better person with no relationships with anyone.
Good luck.