Please steer clear of this word in English if you’re referring to a pain in the neck.
Because ‘cervical’ in English can refer to the neck, but far more commonly to the cervix, please avoid using this term in casual conversation.
So, unless you’re discussing some medical paper (where cervical spine is appropriate for instance), just say you have a pain in the neck or you have a stiff neck.
And by the way, avere la cervicale sounds odd in Italian, too. It’s illogical because if you didn’t have one, you’d have quite a floppy head.