Trying to shove an unlubricated larger penis into you when you are not aroused of course is going to cause tearing and bleeding. I wouldn't worry that something is wrong with you. Just quit having sex with someone when you are "not really turned on"... what's the point?
The cause of cervical dysplasia (which can lead to cervical cancer if left untreated) is the HPV virus. Sleeping with someone who has had a partner with dysplasia or cervical cancer puts you at a high risk of being infected with HPV. You do need to see a gynecologist. Along with your Pap smear, ask for a high risk HPV DNA test to find out if you've been infected with HPV. If you ever get dysplasia, it is treatable. If you don't get it treated, it can lead to cervical cancer. But you have to keep up with regular check ups.