My teenager recently started taking birth control and has had some clotty/thick bleeding for 1 week aprox. Is this normal?

Birth Control. It is common to have a change in the menstrual periods when birth control is started. Good idea to the read the manufacturers information sheet from the pharmacist that comes with the prescription. Have your daughter keep a journal of her menstrual periods and discuss all issues with your doctor to be sure all is well. Keep communication open so that all issues with your daughter are addressed.
Yes. It is common for females to have some breakthrough bleeding once beginning oral contraceptive pills. This should resolve by her third cycle. If it persists, she may need to have the pill changed, and this can be done by her physician.