I bet you're running on pavement and didn't work up to it.
You can push yourself to do the run, but the only way to do it steadily is easing into it.
The shin splints especially are from going too hard to fast, your muscle and tendons are flexing your shin.
So ease up, do shorter runs more often, and build up to and then past what you're doing now. It'll give time for bones to harden, calluses to develop, and supporting connective tissue to strengthen. If there's a park or other grassy area, run on that, it's a million times easier on your body especially starting out.