I'm glad someone pointed out that there are different types and causes for shin splints. Sometimes they'll go away, sometimes they won't, sometimes icing helps, sometimes it doesn't, sometimes during a run they'll get worse, sometimes better.
First, you should try to figure out what's causing them. Go to some running/shoe sites and find out if you're under or over-pronating. It's also possible (as one poster mentioned) that your calves and achilles tendons are too tight and cause too much stress on your shins when they have to pull up on your toe (that's what causes mine combined with under-pronation/supination). Once you've figured out the cause, then you can fix them.
Or you could just suck it up, you're only running a mile.