I had a similar problem at 16. I was scared and didn't tell my mom or go to the doctor. I have my period for months straight, none for months, it would go away a week and come right back, clots like crazy, it sucked. I ended up int he hospital for anemia. Definately go to the doctor and don't be afraid to tell them anything!!! I went on birth control to regulate my period and it worked. I felt normal for the first time. My first internal exam was more embarassing then anything else. The above poster described the visit well. It is over quick, maybe a little uncomfortable, but not bad at all. I hope everything goes well for you!!!
While blood clots are a normal part of a heavier period, that size blood clots and that frequent passing of them is not normal nor is the length of your period. A period should only last up to 7 days, not longer. Your doctor will probably put you on birth control to regulate your periods, and that should make them lighter and a lot shorter (mine went from 7 days heavy with clots to 2-3 days medium flow and sometimes light). Since you've had such lengthy and heavy periods for as long as you have, she will likely also have some blood work done to make sure you have not developed even a mild case of anemia.
I can't say for sure that your doctor will do this as you are under 21 and not sexually active (if you have been before and only mean you are currently not sexually active, you should mention this), but she may choose to do a pap smear to take a sample and make sure everything's alright. In this procedure, they stick a probe inside you and scrape off a minute bit of your cervix for testing. IF she does this, be sure to tell her you aren't sexually active and would appreciate if she uses lube as this will make it a lot easier for you and saying this will likely make her approach a little gentler, too. Also, be sure to breathe and not let yourself tense despite the awkwardness of the situation. Again, I can't say she will do this for sure, but just be prepared in case.
Until you see your doctor, there's nothing you can really do about the blood clots. Is there any way you can be seen sooner (even if it's urgent care)? Or a way you could contact your doctor and ask her to write you a note for you to pick up to excuse you from certain extracurriculars until you see her?
blood clots are definitely a normal thing but having your period that often is something that needs to be checked out. It probably has something to do with your hormonal balance don't worry too much blood clots and heavy periods are a common thing, but nothing you can do to stop it unless you get on birth control to stabilize your periods ask your doctor about it