Glad you found this forum! I can understand where you're coming from. The easy part to address would be to tell you that if your gf was on bc pills that were making her ill (a lot of them do that - crazy stuff those hormone pills) it's not unlikely at all that her missed period is due to recovering from the hormonal rollercoaster.
Or, of course, she could be pregnant. If she's two days late it's definitely late enough to show on a pregnancy test, and over the counter ones are pretty reliable.
You can also go to any Pregnancy Resource Center and get a pregnancy test administered by a nurse for free. They can help you and especially your girlfriend work through any counseling and help needed if she is pregnant and you guys need some support in processing the unplanned news.
I wouldn't worry too much right now about what parents will think. I completely understand how large that can loom, but it's not the most critical thing right now. First find out if she's even pregnant.
If she is - you may have more options than you realize. Adoption, for one, if you just really don't think you can handle having a child together. Financial assistance, for another, if you guys want to make it work.
I hope you'll come back and keep us posted on the update!