Yes, they do hurt when you touch them. No, that is not normal to have tender spots all over your head and neck.
When muscles are problematic they tend to become tight and irritated. When muscles are tight, they tend to hurt right at the muscle belly (the thicker part at the middle of the muscle) or they hurt at the ends of it, where it attaches to bone (the tendon).
In your case you probably have a little of both going on.
Your tight neck muscles may be from posture (too much computer use, for example) or from an injury. Either way, pain and headache is the result. You have many small muscles between your highest spinal bone (the atlas, c1) and your skull, such as your suboccipital muscles. These muscles can become tight and painful and refer pain to areas such as around and behind the eyes. Additionally, your larger neck muscles can cause pain all around the neck, including the top of your shoulders in the “trap” muscles.
No matter which muscles are the cause of your pain, there is something making those muscles feel that way. Muscles are pretty much just levers that move joints and bones, so we need to address the joints and bones that these muscles are attaching to. Adjusting the upper back and neck is a great way to reduce the tension in the neck and allow your spine to relax. Headaches associated with tension in the neck and shoulders can often be reduced or eliminated with chiropractic adjustments. Not always, but often enough to make it worth a try.
Go ahead and rub those tight muscles. If it hurts just to put mild pressure on them, then they are dysfunctional. That means chiropractic can probably help you out. Give it a try!