Recommendation algorithms for social media feeds often function as black boxes from the perspective of users. We aim to detect whether social media feed recommendations are personalized to users, and to characterize the factors contributing to personalization in these feeds. We introduce a general framework to examine a set of social media feed recommendations for a user as a timeline. We label items in the timeline as the result of exploration vs. exploitation of the user's interests on the part of the recommendation algorithm and introduce a set of metrics to capture the extent of personalization across user timelines. We apply our framework to a real TikTok dataset and validate our results using a baseline generated from automated TikTok bots, as well as a randomized baseline. We also investigate the extent to which factors such as video viewing duration, liking, and following drive the personalization of content on TikTok. Our results demonstrate that our framework produces intuitive and explainable results, and can be used to audit and understand personalization in social media feeds.