I am an experienced yoga teacher myself. If you are practicing advanced Sivananda yoga I assume it may include shoulderstand and headstand. Some people should not practice shoulderstand without raising the shoulders on blocks or equivalent and resting the head lower, on the floor, because depending on the length of your neck, you could be overstretching your neck muscles basically causing a whip lash effect. A similar strain can occur if you are putting too much weight on your head in headstand and if you are not completely balanced. The other reason for headaches is overdoing it in strong back bends and creating tension in the neck by overarching the neck by lifting the head back too far. Particularly postures like fish, bow and camel. Sivananda is a traditional form of yoga and in my experience, modifications and props that are essential for some students are not always encouraged, depending on the training and experience of the teacher. You really should not have repetitive headaches after practice so need to sort this out otherwise it might put you off practicing as well as perhaps doing yourself more harm than good. Can you discuss this with your own teacher? Is it worth having a one to one for someone to look very closely at your practice? If you feel your own teacher is not addressing this for you I would explore other teachers / styles of yoga.
Does it happen after you practice certain postures? take care of your breathing. if you´re practicing challenging postures as you say, it could be that you hold the breath, which can cause headaches, could also be tension in neck, so take great care with inversions and postures like shoulderstand, headstand and bridge.