How can I tell whether I have an astigmatism or a lazy eye and astigmatism?

Eye exam. Astigmatism can be checked for during a refraction. Also can be visualized with corneal topography (regular and irregular astigmatism). If the astigmatism was large and uncorrected making one eye weak while the other was strong during visual development, then a lazy eye can happen. Sometimes the lazy eye can drift if not staying focused.
Eye exam. A careful eye exam can help detect astigmatism - regular and irregular and the presence of underlying amblyopia. Sometimes, astigmatisma causes amblyopia.