Continuing to run with shin splints is not a good idea. Continuing the exercise that caused the painful shin splints will only result in further pain and damage that could lead to stress fractures. You should either eliminate running for a while or at least decrease the intensity with which you train.

Do shin splints go away if you keep running?

The pain of shin splints is most severe at the start of the run, but often goes away during a run once the muscles are loosened up.

Can I run a mile with shin splints?

You can run through shin splints, as long as you don't have a stress fracture or other more serious shin problem.