I know it's available over the counter & Dr's don't like to prescribe sleeping tablets. But taking an antihistamine to aid sleep is not a good Idea. After a while they will simply fail to work & if you're not careful you will suffer some severely unpleasant side effects from head ache & nausea to renal problems. They are only safe & effective for a few days use.
Much better to speak openly about insomnia to your doctor. You have an illness that will prevent proper rest & as for not reaching REM sleep is normal for fibro sufferers & therefore giving you something in the long-term far better for your body & the way you feel, no more habit forming if used properly in the short term.
An antihistamine overdose is no way to deal with lack of sleep & that's basically what you are doing, it can make you feel absolutely awful too. Sometimes it's hard to be firm with your Dr, but only you know how you truly feel.