Shy people vary tremendously in how they act in social situations. One may put on an act as the life and soul of the party - another may retreat to the kitchen and stay there until it's time to go home. What many shy people do is leave it up to others to make the running: they leave it to others to be the first to say hello and the first to smile.
The trouble with this approach is that others can misinterpret this as snobbery or hostility. In trying to avoid being seen in a bad light, the shy person ends up creating just that situation. The shy person often fails to realise that others don't actually know that he or she is shy. Because they don't actually know the person is shy, they interpret their silence or reticence as snobbery or lack of interest.
The way to avoid this is to adopt a simple resolution: to be the first to say hello and the first to smile. That's all. There is no need to be the most brilliant conversationalist since Oscar Wilde nor is there any need to knock everyone off their feet with the force of your wonderful personality. Just be the first to say hello and the first to smile.
In following this course of action you are doing something that is in your control to do, you are doing it even though you may not feel like doing it (and so you avoid being a prisoner of your feelings) and you are willing to make a small, practical improvement (saying hello, smiling) instead of building castles in the air.
The silence and reticence of a shy person can push other people away. But you can start changing that now: smile and say hello!