Hello Ewelina,
Thank you for the detailed description of your study. This sounds like an interesting cohort and you have a lot of groups to compare!
You have identified the core issue; due to destructive sampling, the change of timepoint is confounded by the change of animal.
We just discussed what to do with destructive sampling in this thread. You may find it useful:
I again recommend qiime longitudinal first-distances with --p-baseline which is fine for destructive sampling.
Some methods work best with fully independent samples (like you have!) and some work better with matched samples. 
If you have not yet asked a statistician in your department, now is a great time to do so.