Hello~It could be a form of eye strain, although you are not straining your eyes when walking. I suggest seeing your GP, he/she will be able to give you more of an insight.
Also, now that I am thinking about it, you could have some pinched nerves or misaligned vertebrae in your neck, this can certainly cause the issues you are having as well. Possibly seeing a chiropractor would be of some benefit. The chiro will take some x-rays of your neck and upper back, study them and then go over the results with you. A few treatments, should start to help.
Hi there, I am also getting similar headaches frequently. I am currently having painkillers to get relief, hoping to visit a doctor soon.