Why do I have castration anxiety?

Can't say from here. Classically, castration anxiety is understood as part of the oedipal complex, ie., the unconscious childhood fear that competition with father for mother's love will lead to father's retaliation, ie, castration. It's just a theory though, and it may or may not apply to you. More pragmatic reasons include fearful experience or past risk of actual genital damage, scary descriptions, and so forth.
Difficult to answer. The best way to explore your castration anxiety is through psychotherapy where traditional talk and cognitive-behavioral techniques are used. Cognitive-behavioral-- to help you figure out cognitive distortion and to learn techniques of coping with anxiety, while more traditional talk therapy might help bring some of the reasons for your fear to the surface.