There’s more to it than that. Conscience involves a judgment about what’s right or wrong, but it doesn’t work by magic. You first have to form your conscience. This means learning about good and evil, and that’s a job for the intellect.
Many people think conscience is the faculty that tells us what’s right and wrong. That’s a mistake. Conscience is better thought of as an alarm. With your intellect, your mind, you learn what’s right and wrong, and then conscience "sounds off" when you’re about to violate the standards your intellect has learned. If you have no standards, you’ll never hear the alarm because it won’t sound.
But not neglecting the formation of your conscience isn’t enough. You need to make sure not just that your conscience if formed, but that it’s formed correctly. If it is, the moral judgments you make will be reliable. If it is not, your moral judgments won’t be trustworthy.
For example, if you’ve been taught that stealing isn’t wrong and if you really believe that, you won’t have any inhibitions against stealing. Your conscience won’t bother you when you steal because it isn’t reliable when it comes to right and wrong. It’s been formed, but not formed correctly.
It’s true we have an obligation to follow our conscience, even a poorly formed or "erroneous" one, but we also have an obligation to form our consciences properly. For Catholics this means following what is taught in Scripture and Tradition as interpreted through the Magisterium of the Church.