It sounds like you are on the form of birth control
known as Implanon. It is a small device that slowly releases hormones into the blood that prevent ovulation. It uses a progesterone like hormone. This type of device should prevent you from getting your cycle. Thus, it is not surprising at all that you haven't had a period. In fact, I would be more surprised and worried if you were getting your periods. The fact that you have not means that the device is working. Typically (when used and implanted correctly), this type of device has a near zero failure rate. In other words, it is very rare for someone to get pregnant with these devices. Nonetheless, the best thing to do is to speak with your doctor
to be sure. Pregnancy symptoms as you say are often morning sickness (nausea in the morning) and fatigue, which could be do to many different problems. Thus, pregnancy would be low on the list of possibilities in this case. I do think that your issue does need evaluated by your doctor. I suggest that you schedule an appointment with your OB/GYN for an evaluation. If you are truly worried, then your doctor might ask you to perform a simple urine pregnancy test. If this comes back negative, then you should be reassured that you are not pregnant. Then you can look for other reasons why you would be having these symptoms.