Generally 'feel pressured' is when you feel pressured by someone, whereas 'feel pressure' is more general - it might be something you impose on yourself.
"I always feel pressured when my boss comes into the office. I think he is making sure I am working hard".
I'm not sure if you have written what you mean though, in your example. "I always feel pressured to speak in public" means that you feel you are expected to speak in public. If you were perhaps a famous person, then that might be true, if people you know are asking you to give public talks.
Perhaps you meant "I always feel pressure when I speak in public", meaning that you feel pressure to do something, such as speak well.