@peter101,
You are invading her privacy, and it's for almost no reason. As for the reason (that she slept with other guys before you), it's not much of a reason; it's an excuse. Everyone has a past. Don't trample all over her private life because you don't like how she comported herself before you were dating.
If you don't trust her, then don't have a relationship with her. Period. Really, this is not that hard.
BTW, 'girls' (she's a woman, please start referring to her as one) don't like their privacy invaded because they are people and most people don't like to have their privacy invaded.
And finally, both parties in a relationship should be taking responsibility for birth control. Use condoms not only for your own health (yes, even nice people can carry STDs), but also so that you virtually never have to worry about a pregnancy scare ever again. Yes, condoms can fail. No birth control method, other than absolute abstinence, is utterly, 100% reliable. But using a condom is better than nothing and it gives you some control over a situation with someone who you clearly don't trust.
After all, if she is as unreliable as you seem to believe she is, a kid would be calling you Daddy by now.