You guys are obviously young and somewhat immature, and probably have no idea what you're doing. If her parents are super christian then she probably knows nothing about sex and you don't seem to be an expert yourself, no offense. Here are some things for you to consider (I'm a medical student, I work in a gyn clinic and I teach sex ed so I kinda know what I'm talking about here):
1) She should establish care with a gynecologist just for general health reasons unrelated to your current issue. I'm sure this can be accomplished at PP.
2) PP deals with young patients in sensitive family situations all the time. You and your gf should talk to PP about her options for not letting her parents know. Depending on the way billing works, her parents may get a bill from PP but it won't say what they did, because that is protected health information that her parents don't have a legal right to access.
3) Her university probably has a health clinic that can accommodate her needs and may be a more palatable source of women's care than PP to her parents.
4) You can't force her to use bc. As many other people in this thread have said, Plan B is not good to use consistently. It's like an overdose of birth control.
5) If she is concerned about the pill in particular, please let her know that there are other, easier alternatives.
a) Nuvaring (apparently this may have some increased risk of clotting but it's not recalled or anything) is a soft plastic ring inserted into the vagina for 3 weeks and then removed to allow for menses.
b) Mirena is an IUD, a soft plastic T-shaped insert that goes into the uterus and stays for years. It's really effective and also can reduce or eliminate periods. It's hormonal though, so some women have adverse effects from that.
c) Paragard is also an IUD but it uses copper instead of hormones. Really effective, most women still get periods, some women get bad cramps or off-cycle bleeding from this.
d) Nexplanon is a plastic insert placed in the fatty tissue in your upper arm. Really effective, stays in for a few years, easy to place and remove. Also hormonal.
Please please please educate yourselves before you guys do something stupid and get pregnant or some shit like that. PM me if you need more guidance.