Why is the cervical cap causing irritation?

The irritation could be from an allergy to spermicide.
Try this: if the irritation is not too bad, you might want to try another brand of spermicide.
Still not working? If you have tried different types of spermicides and are still having irritation, try a method that does not require any, like the IUD, injectable, patch, pill, ring, or implant. If you want to stick with a barrier method, you could try non-spermicidal external condoms (male).
Try a different method: implant, IUD, condom, Patch, Pill, Ring, injectable.