Search for your journal title (NOT article title) below, in Ulrich's.
If the journal's record indicates it is refereed, it's likely (but not guaranteed) your article has been peer reviewed.
These databases limit their content to particular areas of study:
What should you do if you find an interesting article in a database but no link to the full text?
Click on the purple "Check for full text" button – this button will attempt to connect you to the full text article if it is owned by the UW.