You can play your own missions, but I'm thinking the reason you can't is one of three things.
1. Is the mission published? During July and parts of August, the Foundry was experiencing some serious issues and I think some missions were taken down. Try republishing the mission and then search for it.
2. Your mission didn't have 5 reviews and is still in the review status. When you open the tab to search for Foundry missions, click on the button on the bottom of the screen to "Start Reviewing". Then in the new review tab, search for your mission.