While frame geometry between different manufacturers can vary, it typically is similar enough that if you're a woman's small on a specialized, you will be a woman's small on any brand. My girlfriend is 5'1" and she rides a women's small, based on your height alone you would likely be a woman's medium. However depending on how long your arms/torso are, that may vary.
But my recommendation is that you go into a decent bike shop and have them size you properly. That way you will know what you're looking for when you are ready to buy something.