Design Project Management - how do you do it?

Designers (just like developers) have a particular set of projects for which an agile approach is more suitable. But this is not a rule. In your case if you need to manage multiple projects that share common resources and you would like to see when those resources get overallocated you might want to try RationalPlan. It is easier to use compared to MS Project but not very suitable for agile as it is Jira.