You would do well to try and develop what friendships you can manage to have, while you are pursuing your doctorate. You're ability to relate to other people will be just as important to your later success in what you do professionally, as your academic achievement.

If you run this question by the chairman of your department, I'll bet you get told what I've just said. Part of the goal of a doctoral program is to make you a generally well-developed human being. That's why you are required to take some courses that are outside your area of specialization. The program, in general, is supposed to contribute toward your overall maturity. This implies social maturity, as well. By now, you will have noticed that activity in your department specifically includes things that promote social interaction among faculty and grad students. You've probably been invited to the homes of professors. It is now that you start making professional contacts that may help your career. More importantly, it is now that you learn to be part of the collegiality that is part of being a professional.

If being social is challenging for you, now is the time to be working on that. Three years of isolating will just slow down your general progress in life.