Hey: you can't make other people's birth control choiuces for them, and it isn't your place. In general, when you're trying to doictate very personacl choices to someone else, they ARE going to tune you out in pretty short order.
Hormonal copntraceptives are not right for everyone and DO carry side effects. Not wanting to use them -- or any given method -- is totally valid. Heck, I was on the pill for cramps way, way back when for years and while I recognize that it works well for some people, I sure wouldn't want to be on it again. What method is best and desired varies from person to person.
Condoms, used properly and every time, actually are incredibly effective birth control all by themselves, right here, "in the real world." In the case breaks do happen, EC is also available. So, it actually isn't neccessary to use hormonal birth control to have effective birth control. Condoms work perfectly well on their own, and if she wants backup, there are methods available which are nonhormonal.
You're her friend, not her mother, darlin. You can't force a friend to use methods you'd choose to use, nor even to be responsible. As a friend, what you're better off doing is offering help she actually wants from you, and that isn't invasive, like, say, the two of you making your annual GYN exams together as a friend date, and she can discuss birth control options with her doctor or clinican there.