Is it normal for head/neck pain to come up every time I exercise?

No. You should be able to exercise without pain. If your head/neck hurts wtih exercise you may want to see your md for an x-ray. You may have some arthritic changes in your spine leading to the pain.
No but it may be due. To how you are exercising rather than related to anything wrong with your neck especially if you have no symptoms otherwise. You may need instruction on your form or you may be just over doing it. Did you recently just start exercising? This nay also be a reason and you are just deconditioned, possibly. If it persists, see your doctor.