Condoms are less effective than the pill in preventing pregnancy, but more effective at preventing STDs. Correct use helps condoms be more effective (making sure that they are used before the expiration date, not storing them in a warm place such as the car or wallet, using lubricant under and over the condom to prevent breakage, etc). If you are really worried, I would suggest going to the doctor and asking about other methods, such as a diaphragm.
Condoms are a good option for people who cannot take the pill, but there are other options as well. Talk to your doctor about what is most effective for you. While abstinence is the only 100% guarantee (besides sterilization, of course), try exploring other routes before you choose that. Also, there are several types of birth control pills. Maybe another type would give you fewer problems.
Good luck.