Meaghan,
First, I want to congratulate you and offer support for the wonderful job you are doing as a mom navigating this issue with your daughter. It can be terrifying for us moms, no matter WHAT our personal experiences with sexuality (and our own moms) have been, when we simply even start thinking about all the many worlds of complexities our daughter's sexuality may bring. It can also be tempting to pretend and hope that she will simply listen to you and not become sexual until you approve, so I applaud you for being straightforward and open with your daughter.
I hope she does not choose to be sexual with her boyfriend unless they are very much in love with each other and are emotionally ready to handle the intensity of the relationship once it goes there. I also hope you and she have discussed what happens if birth control, for whatever reason, fails, and she ends up pregnant. Because it can--as the person posting below me can attest. As a perinatal counselor, I have found myself working with many very experienced, mature women who ended up pregnant with various methods of birth control that they definitely knew how to use.
So, your question...I don't know what the age of medical consent in FL is--whether that is a federal or state thing, though I believe it may be federal, since HIPPA is--but in Oregon, the age is 16 that a patient's medical records may not be released, even to the parent who is paying the bills and raising the teen, without a consent form signed by the patient.
If you allowed your daughter to go into the consultation on her own without at least requesting that you be able to participate in some way, the doctor probably assumed you were aware of this and did not offer any information. In addition, since the visit was so short, you might assume that your teen daughter, who is still a teenager and probably NOT all that into talking about sex with an adult, probably did not volunteer that she wanted her mom to come in with her, and probably did not ask a lot of questions.
What I would suggest is that you ask your daughter if she would sign a release of information for you to be able to speak with the OB/GYN. It sounds like you have a good relationship with your daughter about this, and it would be easy to let her know that this is just so you can help her with her budding maturity.
And yes, you know her best--not her doctor. If you know that she is not all that reliable about taking medication, you definitely should work out some way of reminding her that you both feel comfortable with. AND remind her always that, just because you have helped her get on the pill, that doesn't mean sex is right for her, AND remind her that even on the pill, people can get pregnant OR get diseases, so a condom is an important backup. Make sure she knows how to use one properly, as many teenage boys don't.