Gym is great, but I would strongly advice going into martial arts classes, for examble thai-boxing or jiu-jitsu. You'll get a boost in self-confidence overall, but also will learn how to communicate with other people when being split to pairs for 1x1 training. That will help combating a lot of social awkwardness and inabvility to speak to new people.

Another one is: try getting into more managerial position at work — that naturally implies more communication, meetings, presentations and such, so you will learn by practice.

Speaking from personal experience, also being shy initially — still am but much much less, it is practically a non-issue anymore.