There might be more than one thing.  Concerning the shooting pains and back of the skull, I was having that off and on this year, very frustrating, went through sinus scan, ultrasound of my neck, ya da ya da, nothing.  My doctor asked for MRI, insurance wouldn't do it, (and actually I don't blame them).  I finally found a chiropractor who said I had 'sub-occipital syndrome'  or occipital neuralgia, and suggested some simple exercises that were almost exactly opposite what the P.T. people were having me do (some of what they did helped the muscle spasms but not all of it, and not the shooting pain totally).   It's kind of like piriformis syndrome (sciatic nerve going though  buttock/thigh muscle) in that there is a nerve going through the muscles around the neck and the muscle spasms irritate the nerves, that causes more spasms, and so on, a vicious cycle. It sends pain right up into the head, temple, even in your eye and can affect your vision (P.T. told me that too).  What helped was - not trying to work it and stretch it out, that makes it worse.  She had me clasp one hand on the other wrist with almost straight arms behind my back, and lift my arms a little, at the same time flex my neck (gently for us RA folks - check with your doctor first, this is not for everyone...) to rest the scalene muscles.  Do this maybe twice a day for short time: she said 30-40 seconds, I started with about 10-20.  Don't over do it.  If you have serious neck arthritis, don't do any flexing of neck without checking with doctor, as some RA patients have serious cervical deterioration (I checked and I don't).

     The other thing that helped was, just knowing what it was, and NOT to try and stretch, but relax.  I was making it worse.  It seems to be not happening now (keep my fingers crossed!)  I don't do the stretch very often, but at least I know how to help myself now.

     hope this helps.  Again, if you haven't been evaluated with imaging, physical therapist, or whatever, you might want to try that first.  Make sure there's no structural cause. If there is some kind of pressure on spinal nerve, maybe it would also affect the chest, I don't know.  If it's functional, P.T. might help completely.  If it a combination of muscle spasm/nerve irritation, then relaxation is important.  A muscle relaxant might help, but you may also need to change the way you use your muscles - posture, rest, breathing etc.  Meditation, tai chi, can  be helpful but therapy may also be needed.  I am not a medical professional, but I am a fellow sufferor of long term!