Yes to new shoes and rest. When I ran in high school, despite having some vicious shin splints. There were very large and discernible bumps on both shins. My guess is that they evolved into stress fractures. I was very stupid back then--and had a bad coach who thought it was a sign of commitment to run through pain. I also ran with stress fractures in my feet. It's no wonder that it took me years to want to run again!