If she 'feels' she can go to her mother, then that may mean that she and her mother Normally have a good communication history. This is important, and great, if she does. Then, by all means, she should talk to her mother.
IF not, then follow the suggestions of the others to go directly to her doctor, or planned parenthood. However, if she goes directly to her doctor, then the parents may find out anyway - who is going to pay the bill - he may send the billing directly to the home, as with any other bill.
If she wants to keep it secret, then go to Planned Parenthood.
However, direct communication with the parents - mother (she will most likely discuss with the father after wards, but maybe not).
If her mother is a sharp, common sense type person, she is going to Realize that once a daughter, or son, becomes sexually active - telling them No, you can not do that, is ridiculous!
She will not want her daughter to get PG, and the only sensible thing is to arrange a doctors appointment, give her permission to the doctor to prescribe birth control pills and move forward.
AND, you Both are Super responsible to want and to follow thru with getting a reliable birth control. It will protect you both from screwing (no pun intended) up your lives with a child early in your lives.
Having said all the above - let me state this. My wife and I raised Two daughters. We always made it Clear, that we did not encourage early sexual activity, but neither were we dumb. And that No one in the family wanted either of them becoming PG, because if they did, then raising the child would be Their Responsibility. And that we would continue to provide the necessities of life until they graduated high school, after that - we expected them to be adults and be fully responsible for providing for the child and raising it.
But at the same time we told them the above, we also told them that we 'wanted' them to come to us, their mother in particular - at first, and Tell us that they were planning to become sexually active, and ask for our help in getting them to a doctor and getting proper birth control so that all of the negative repercussions of being sexually active did NOT occur.
Guess what - shortly after our oldest daughter turned 16, she did come to her mother and told her - it is time. Can we make an appointment to go get birth control pills, etc.
Granted my daughter, like your gf, was nervous, but when she came to her mother and they discussed everything - there was NO yelling, NO arguments, No saying you can not do that, although we did Not like the boyfriend that she had at the time. We were all realistic, common sense, and protective. Three days later, she had her doctors appointment, her mother went with her, and she got the pills.
That's the Way smart parents and families handle it. Not all parents are smart and logical, and realistic. But that is life, and proper communication and 'protection' is the way to go!!!
I Hope your gf can do the same with her mother, otherwise go to planned parenthood. Be Safe - you two are smarter that the average bear - teenagers!!!