Sounds like you are dealing with a lot, I can definitely relate, I used to have horrible sleep problems and could only sleep 4 hours a night on sleeping pills. Just one thought, waking up with a racing heart and chest pains can be a symptom of GERD, reflux always makes my heart go crazy and during the night is quite a common time for people to get reflux.
As far as starting to fall asleep and then suddenly feeling unwell and dizzy, I've had this too and it was my anxiety. My body was in permanent 'alert' phase and whenever I needed to go to sleep it would do this to wake me up as it thought I needed to be up and awake for whatever danger it perceived.
Waking up after only a short sleep is also a symptom of depression, you should let your doctor know, because anxiety, not sleeping and depression all go hand in hand. My frequent waking during the night only really improved once I was on antidepressants and tackling the depression. There are also some antidepressants that are good for pain relief too, so can help with the fibromyalgia, tricyclics like nortriptyline.
On thing that really helped me overcome my sleep issues was Autogenic Training. It is very effective for pain relief for fibromyalgia as well. Its a sort of self hypnosis except its not actually hypnosis its just relaxing different parts of your body and making them feel heavy and warm. I did this at least 6x a day when my sleep was at its worst and it really helped. Not only did it help sleep, but it helped me not feel so tired during the day. When I couldnt fall asleep I would do this for hours just lying in bed and it would really rest my mind and body without the need to actual sleep, next best thing so to speak.
Here is the book I used to teach myself Autogenics https://drive.google.com/file/d/0B8lwT7_ft9E4VE9qaFJwVFp0LUE/view?usp=sharing
Thank you for your response! I know that GERD can cause chest pain, but I've never heard of it causing a racing heart. It makes sense though, so perhaps that has something to do with it. I am taking 40mg of omeprazole everyday, so hopefully it's helping some. I'm not depressed, but I could still have some underlying anxiety disorder. I was diagnosed with Generalized Anxiety Disorder when I was 17. Fortunately, an antidepressant and CBT seemed to help my anxiety tremendously; however, I have been off of the antidepressant for a couple years. I'm considering getting back on one to see if it helps! I know some can help with pain relief, so I will consider some of them. I will definitely look into the Autogenic Training. It sounds interesting and perhaps it could help with some of my sleep issues, as well! Thank you for the advice.