As an Inspector on a Team, you can schedule jobs for yourself. Without the permissions of a Team Owner, you can't schedule Jobs for anyone else on your Team, but you can schedule your own Jobs.
When you follow the usual steps to Schedule a New Job, you'll see that the Job is automatically assigned to you.
Once the Job is created, it will behave just like any other Team Job. Your Team Owner can add additional inspectors as needed, and you'll have all the same permissions as you usually would in your Team.