SS
Shin Splints isn't in the bone mate, its the soft tissue surrounding it. I've had it before and must admit when I read your post I immediately thought "Shin Splints!" Its an intense burning sensation and strikes as you mentioned in the lower half of the lower leg, can happen in both legs at the same time. It used to feel like somebody was holding a flame up to my legs. It repeats on itself if not treated and can cause ongoing problems.
Some people sometimes think they have shin splints when they actually have a stress fracture - similar type of pain apparently - but as you have it in both legs that must be nearly impossible...
I got it when I used to run on the roads, my trainers were all wrong, its linked to gait, technique, comeback from injury, all sorts of stuff. Its treated with rest, ice, and something like Ibuprofen to take any inflamation out (you won't necessarily notice any inflamation, but its there causing the pain), and once rested building up intensity and frequency of training gradually. Oh, and I swapped my running shoes.
Obviously I'm not a physio or qualified bod so this is just a 'off the top of my head' kind of post, but from what you said it seemed to fit. I certainly wouldn't rule it out. Here is a good link from some guy in the US that will give more info...
http://www.watfxc.com/TF/TF%20Educat...in_splints.htm
All the best
Simon