No, it's not just you! TestFlight is currently down for some users, including yours truly. While Apple took a bit of time to acknowledge the issue, the System Status page has now been updated to reflect the issue.
Update: the issue has now been resolved!
According to Apple, the issue started at 8.35 AM Pacific Time and is currently ongoing. Â The company notes that "Users are experiencing a problem with this service. We are investigating and will update the status as more information becomes available."