Your girlfriend's trust issues may (or, may not) have anything to do with you. Have you ever cheated on her? When you're watching these programs, do you make comments on how these women look, like, "Whoah! She looks GREAT!" or compare her appearance to the women on the screen? What are you two doing to support yourselves? Are you each pursuing your educations? There is so much information here that would have a direct impact upon your situation.
Yes, she's quite insecure, but there's a reason for her insecurity and there's something more to this than meets the eye. Personally, at 19, I wouldn't be living with ANYone. I got married at 23 and I still made a very stupid mistake in choosing my spouse. LOL!!!!