YYC, one of the first questions my rheumy asked at my initial appt. with him was how was I sleeping. I told him I often woke up in the night stiff as a board and aching; he prescribed Flexeril, a muscle relaxant I take 2 hrs. before bed. It does tend to dry the mouth -- not good for Sjoggies -- but it's a trade-off. The dryness was worse when I first started taking it.
I get 'pins and needles' in my feet and legs, plus sometimes the 'numb feet' feeling when I've slept poorly, so I know in my case there's a direct relationship between the quality of sleep and how I feel.
Since 1981 I've walked 2-3 miles most mornings and been in a twice-a-week exercise class -- 20 years before my SjS Dx. I think it probably has helped me overall. I still walk, though not as far or as fast and the exercise class emphasizes stretching -- including a few yoga moves -- rather than aerobics.
The dr. is right

that exercise would help you feel better. Maybe you can figure out something that doesn't make you feel so awful when you get done. Have you tried walking for one block for a week and then adding a half-block more each week until you work up to about 20 minutes? I know I feel better after I'm done; the first 10 minutes of my walk I often drag along. Or maybe a few yoga stretches would be possible. There are DVDs for beginners.
Right now, my GP is trying to figure out what's causing pain in my left shoulder and upper arm. When it's really painful and I can't get comfortable in bed, I don't sleep much and my SjS symptoms are worse the next day. Talk about a vicious circle...
I sympathize with your pain and hope you'll get some help with yours.