Accounting for correlated data within a group

I am trying to analyze data that has a pre, post, and follow up time point. However, within each time point I also have pairs of correlated data due to analyzing the right and left sides of an individual (not everyone, but about 80% of the data has a match). I'm working with a rare disease so I want to be able to use both sides of an individual.

I was using a repeated measures (Kruskal Wallis) to account for the correlation between time points but I'm not sure how I go about accounting for the paired data within the time points. I've come across GEE but that seems to be equivalent to running a regression model and I am looking to compare the means (medians) between time points. Any guidance is greatly appreciated.