Forget about what the distribution looks like. Focus on what you are interested in finding out *without regard to what the data happen to look like*.
Presumably you're dealing with paired data, so you'd be interested in demonstrating something about pair-differences -- e.g. a mean change (after-before difference), for example - focus on that information. If you particularly want to also summarize the before and after values themselves, choose measures that relate to that difference of interest.