There are other options, if you are a student enrolled at a large college a number of them offer very cheap student health insurance that can cover your birth control, also if you have a health clinic on your campus you can get your birth control at a really low price.
Nuva Ring is still a hormonal for of BC, so if you have had problems with hormone based BC you may want to investigate a little more. The only difference is really the route that you get your hormones. It simply absorbs into the blood supply from around your cervix. A friend of mine tried it and complained bitterly that it slipped out a lot during sex since they dont make the Nuva Ring in different sizes.
Other options you can consider:
IUD - great if you dont have plans for the next several years. The cost is high comparatively to pills but you don't have to think about it for a while and Planned Parenthood actually subsidizes the procedure. Call your local PP and see what the price is. The advantage to this is that there are no hormones in an IUD, if you are really sensitive to hormones it may be a great option for you.
Female Condom - It is the 21st Century and yes girls can wear condoms too. They can be purchased relatively cheaply at Planned Parenthood link
link
Cervical Cap - the modern version of the diaphragm, Fits over your cervix and you can get one for about $50-60 and it will last for about 2 years.
You can also use the sponge with spermicide or the Ortho Evra patch.
Also go onto PP's website and use the online booking, that way you can get an appointment way in advance to your liking. If that doesn't work, google search to see if there are any other low income programs in your city. Many County run or community hospitals will have womens health clinics or at least some resources on where to get free or low cost birth control