Yes. It is possible to cause headaches. Usually, for people who suffer blocked tear duct, their tears can't drain out normally, which likely cause watery and irritated eyes. In this ways, swelling eyes, blurred vision as well as headache often occurs to. So, you shall not underestimate the damages of blocked tear ducts. Just go to see a doctor.
Well, it seems that you are quite worried about the problems that blocked tear ducts could bring to you. Anyway, once got blocked tear ducts, your eyes would be constantly watery without stop, and sometimes it could lead to dacryocystitis. But there are few cases that it could make your headache. Because it is a problem with your tear ducts, not your brain nerves.
Yes, it is very possible for you to get headaches because of the blocked tear ducts which your eyes can't emit the dirty things out of the eyes normally. Your watery and irritated eyes will cause the disorder of the eye nerves. As we know, the whole nerves in the body are interlinked. Thus the bad eye nerves will affect the brain's nerves. That is why you get the headache. You'd better use the warm compress to make the eyes feel comfortable. You could also use some eye drops to release the symptom. You'd better not eat the spicy or irritating food which will make your eyes get series. You should have the good sleep to offer the good rest for your eyes. Only after you cure the blocked tear ducts can you have no problems at the headache. You could also take some medicine with anti-inflammation to cure the blocked tear ducts.