TikTok doesn't have a default Watch History feature that will allow you to do this, but there's a good workaround. It takes time but it will allow you to see the videos you've already watched.
First, open TikTok and tap the Me icon to go to your profile.
From here, go to Settings (three vertical dots on the top right) → Account → Privacy → Personalization and Data → Download your data.
Tap the Request data file button. Your request will be pending in the Download data tab until it's ready, which should take a few days. You can retrieve the ZIP file once the Pending on the button changes to Download.