Yes! If the shape of the helmet is not right (too round, for example) or if it is too tight.
Yes you can 😅 When your helmet is to small for your had or the quality of the brand where your helmet is from ist very low/bad 😕
If the helmet is too small for you or you wear it for a very long time it could give you a headache but other than that I don't see why.
Sometimes it could also be from the way your hair is, or your hairnet if you wear one.
I agree with Amy that you shouldn't get a headache unless the helmet is the wrong size for you.
I believe that you can have a headache only if your helmet is too small for you ! I cannot see any other explanation 🙂