Outside of my shin, in the muscle, not the bone. I stretch until the cows come home which is perplexing to me because it doesn't feel like it helps. It doesn't really work out for me to ice my legs when I'm out at the track either unfortunately. I was evaluated by a glorified salesman who measured my arch, my walk, said I rolled my ankle when walking, and then submitted a group of 4 different shoes to me of which the Brooks felt the best. Maybe a true physical therapist is up next if my shins don't start feeling better.
Okay, so I was thinking about this some more, and I might be confusing two distinct feelings (I'm not a PT or anything, so I lack the training to distinguish the two). When you say shin splints, I usually think of nagging, fairly low intensity pain that lasts "forever," usually on the inside of your shin. For me it was probably caused by poor form and bad shoes. However, you said that the outside of your leg tightens up and that you're usually good to go after a few minutes if you stop. That sounds like something I used to get a lot in high school (the outside muscles of my lower legs would be constantly engaged like in static contraction after a few minutes of running, so it was rock hard and I couldn't move certain parts of my feet -- hurt a lot, but usually I would fight through it and after 10-15 minutes I would be fine again), but by college I figured out how to avoid them almost entirely. I know shin splints are a generic term, but I think the mechanism behind this type of pain is different (SC will be able to comment on this more than I can).
So here's what I noticed:
1) I would usually get them after NOT running for a few days (most of the time I would get them on Monday, since Saturday and Sunday were off days if we didn't have an invitational).
2) I would usually get them if we were doing something fast, like intervals or a tempo (we had workouts on Tuesday, but occasionally we would do something fast on Monday as well). Sometimes it would even happen if I took the warmup too fast.
3) I would usually get them if I didn't eat enough before going to practice.
I just took care of these in the most obvious way possible:
1) Took only 1 day a week off. Saturday would be easy and short if I didn't have an invite, but I would still run a bit (~2 miles? not very much).
2) Took a longer, slower warmup before intervals. I would probably warm up for 10 minutes longer than everyone else. I would get to practice early to do this so I could still work out with the team for most of it.
3) Brought a lot more food to school. I ate bananas since they were convenient and I heard potassium is good for stopping muscle spasms, but I think really anything would have done it.
After doing this, I would get that static contraction feeling maybe once every few months as opposed to the 2x a week I was getting in high school -- and that was usually right after I would break one of the rules above (i.e. taking 3-4 days off, or running the warmup far too quickly, or not eating before practice). Again I'm not sure if this is really the same thing you're talking about, but maybe there's something there that can help you.