We have some information on all the forms of birth control that might be available to you here; it might help to take a look at those options and see if any look good to you:
Birth Control Bingo! Given your desire to have your method be private, you may find an IUD or an implant to be worth looking at.
A tricky thing about birth control methods is that you can't necessarily predict if you'll experience a side effect before trying a particular method, and that can make it stressful to try out new ones. If you have questions about any of those options, or there are any other things you want to ask about that might help you make a further decision, we'd be happy to discuss them with you.