That actually sounds like digital eye strain, and yes, it's real - not just something you're imagining. Half a year is definitely long enough to do something serious about it. The answers so far have made good points, but I'd start differently: before you run off to the optician, try the basics first. The 20-20-20 rule actually works - every 20 minutes, look at something at least 6 meters away for 20 seconds. Sounds simple, but lots of people don't do it because they forget. On top of that: check your screen height (should be at eye level or slightly below), adjust the room lighting (not directly behind you, better if it's diffuse), and turn down your screen brightness - a lot of people have theirs way too bright.
Now about glasses or contact lenses - that's important, but not necessarily the first problem. If you've had yours for a while now and the headaches only started half a year ago, then your eyesight probably hasn't changed as much as your work setup has. Often when you're looking at a screen for long stretches, headaches come from tension in your neck and shoulders - the eyes get blamed, but your neck is clenched up. Make a conscious effort to sit looser, do some stretches in between.
If you don't notice any improvement after 2 or 3 weeks with all these adjustments, then go see an eye doctor or optician - not because it's absolutely necessary, but to be sure. But don't jump straight to big measures; start with the simple stuff. And if the headaches get really intense or feel different than they did at first, then actually see a doctor, not just for your eyes.