Most Kundalini headaches are caused by too much energy in the head. Many people are accustomed to releasing energy downward, into the Earth. This works if they are spiritually awakened, but not Kundalini awakened, or only using prana.
Kundalini moves upwards. When Kundalini clears karma, the debris exits out the crown chakra at the top of the head, like smoke out a chimney. If the crown chakra is closed, then the energy gets trapped in the head, like a room gets smoky if the chimney is blocked.
Most headaches can be alleviated by opening the crown chakra. There is a crown chakra opening visualization at the beginning of the grounding meditation. Just imagine that the top of your head is a flower bud, and imagine the flower opening and the headache blowing away like pollen. Chakras are often symbolized as flowers, the crown chakra is called the thousand petaled lotus.
Aside from that, Kundalini alters the bones in your head; some yogis even develop a fontanelle like a baby's soft spot on the top of their head. If some of the bones in your head are stuck, consulting a cranio-sacral therapist can put it to rights. Headaches can be caused by vertebra in need of chiropractic adjustment. Regular visits to a chiropractor are a good idea in any case- Kundalini likes a straight spine! You may notice your spine makes some cracking and popping noises when you have kriyas, as it straightens itself.
Don't be shy about taking a pill, if the pain makes it hard to focus. Aspirin, Ibuprofen, Tylenol,... Goddess provides these medicines for your need, and it is not wrong or weak to use them.
Of course, headaches can have many sources, and it is advisable to consult a physician about any symptoms that persist.