The best way to check your artwork approval status is to keep an eye on the Approval Indicator for the artwork in your Campaign’s dashboard. This gives you a view of whether that specific artwork is approved to run for that specific campaign, while targeting that specific list of publishers:
If you have created a campaign already:
I use a modified traffic light system to denote ad/artwork approval status:
Just as a note - If you haven’t created a campaign and have simply uploaded an artwork in the Gallery, then you won’t be able to see a full approval status for the artwork since it will not have been targeted to any specific publisher - not until it has been used in a campaign. So go ahead and create a campaign first.