Could my newly painted walls be giving me a headache?

Paint exposure. Yes. Exposure to chemicals in paint can cause headaches and other illness.
Headaches. Fumes from the paint could cause headaches. Ventilate the room for a couple days and then see if that helps. In the meantime avoid all headache triggers. Avoid caffeine, drink water, excercize, sleep regularly, eat three meals a day, decrease stress. If after doing all these things and headaches remain see your physician.