You live in the US. If you have any kind of health insurance, birth control is free.
You don't have to talk to either of your parents. If you can drive or get a ride from someone, go to Planned Parenthood. Everything about your treatment there is confidential, and they will usually give you free birth control. I got a year's worth in one visit. If there isn't a Planned Parenthood in your area, many women's health clinics offer similar services at low or no cost. If you need to talk to your mother, just tell her you need to regulate your periods. Birth control is often prescribed for this purpose.
Tell her u want it for ur cramps ur parents only worry is going to be pregnancy re assure them u want it for ur periods plus it will help regulate them