What you are likely experiencing is a caffeine withdrawal headache
. They are very common because a huge number of people (including myself) consume enough caffeine that when we go without it, there are symptoms. This can occur with coffee, tea, soft drinks or any other type of caffeine containing product. Basically you have two choices. 1. You can quite caffeine and tough it out for a week or two when the headaches will go away, or 2. You can go back to your routine of drinking coffee. There is a third option which is to systematically decrease your caffeine intake every day which can help prevent the headaches as you get of caffeine.
I should note that there are advantages and disadvantages to getting off caffeine. Consuming too much caffeine has been associated with high blood pressure
and difficulty sleeping. Thus, if you can stop drinking coffee, it will probably be better for your health. I should also note that drinking coffee has been associated with lower rates of Alzheimer's disease making it a tougher decision.
I suggest that you schedule an appointment with your primary care physician
. The two of you can discuss the pros and cons of each option and decide together what would be best for your health and happiness. Good luck.