They should be snug, but not painful. As for your pain, Is the helmet tight all the way around, or does it squeeze your head in a specific direction? I have a long head and a lot of helmets are way to tight on my forehead. About all you can do is get a brand that fits longer heads. Bell are generally quite round, for instance. I have some difficulty one that is even reasonably comfortable, although the Apex does work for me. A 500 doesn't. For open face helmets, the Fulmer fits me great, far better than the Bell 500. The problem with Fulmer is that you have to find a shop that carries them as they don't sell them online. They want to make sure you tried it on before you buy.
I had an AGV full face that was quite tight, but not terribly uncomfortable. It was tight enough on my jaws to give me a case of TMJ, which is pushing on my jaw hard enough to knock it out of joint. Now that got painful. I quit wearing the helmet and it went away. I went back to it later and all the previous wearing had loosened it up enough that, after the jaw healed up, I could wear it again. I ended up going over the handlebars when a car T-boned me and wiped it out.
Saved my head, though!
Bare