about 13 years ago I began having the same symptoms you describe. Double vision is a major pain in the neck, but I found a good ophalmologist who added prisms to my eyeglass prescriptions, and as long as I get regular eye exams (which we need to be doing anyway if we're taking plaquenil) and new prescriptions as my double vision worsens, I'm fine.
I did, however, also go through the same problem with reading that you describe, even though I could see perfectly with my glasses on. My eye doctor recommended that I purchase a Kindle, which I did. Within the first week I was able to read three books. It was like a miracle for me. I can't explain it, except that since I enlarge the font quite a bit, there is little on the page to distract me.
I think that my difficulty with reading was not related to my double vision, or weak eye muscles, but rather, as Lynnwood describes, it was because of lack of concentration. Or perhaps brain fog.
I hope you'll see a good opthalmologist, and preferably a neuro-opthalmologist and get a new script for your glasses.
BTW, I use a MacBook, and with a touch of my fingers, I can enlarge the print, like you can with an iphone, and that also helps me a lot.
SLE, fibro, renauds, restless leg, hiatal hernia, double vision, migraines, costocondritis.
plaquenil, neurontin, synthroid, triamterene, actonel, niaspan, lyrica, tri-est, cymbalta,