I've had what I thought was posterior shin splints, had thought this was what I had for just over a year and read up on what to do and so on. Turns out it was a stress fracture all along but meanwhile I had gained a bit of an understanding about shin splints.
I had decided that it was impossible to stop all exercise, not just the psychological side and fear of weight gain but also because I do not own a car or a bike or have a taxi service. I have to walk alot day to day even just to get the train or bus and quite frequently throughout the day. Resting was not an option.
So I worked out that shin splints are aggrivated by the muscles being inflammed and also by impact. Running causes an impact as you can imagine, its probably the worst type of exercise you can do.
Walking also used to hurt me but as I say, I had a SF and not SS so it may well be different. What I did fine was that wearing trainers rather then smart shoes or flat sandals (or ballet pumps or anything else which isn't made from a wedge of soft rubber) would hurt, so switching to trainers could help as well.
Pill wise I used to take ibuprofen, I'd read this helped because it reduced the inflammation and this itself also worsened the SS as it would further inflame the muscle which would in turn pull away from the bone and so cause further problems.
I also used to wear a compression sleeve. This did help (so also helps SF and not just SS). I got mine from Runners World for about £10, called 'Vulcan' or something like that its blue and made with velcro straps and they also make them for ankles and knees and so on but only some branches sell them. I do think it was worth it though as it worked far better then any of the white stretchy bandage type support wraps you can buy elsewhere.
I also found sports massage helped. Don't ask me why, I don't know! I have theories about it increasing the circulation and I do think that good circulation is key as it carries away any damaged cells and helps replenish with new working cells to speeds up recovery. I also think it helped by releasing some tension I'd built in my calves and quads and losening things up which possibly meant I was using those muscles properly as oppose to pushing more stress onto the already damaged areas which possibly had become damaged party due to repetative and undue tension.