“Could I get a prescription for birth control as easily as walking into a clinic and asking for one?”
In most states, the answer to your question would be yes. The federal law allows for women to seek services for family planning and testing for sexually transmitted infections if they are 13 years or older. In most states, the state law will follow the federal law.
The problem for young women is that if they do not want their parents to know that they are sexually active, your insurance will send home an explanation of benefits (EOB) that will tell the parent(s)
that their daughter was seen in the clinic but will not tell the parents what the visit was for. The parent(s) may ask their child why they went to clinic so, if there is not good communication between the adults and the child, things could get messy!
You want to find a clinic that is youth friendly. The website Advocates for Youth has lots of information about teen rights and youth
friendly services : https://www.advocatesforyouth.org/