Hmm. There are a few social media management platforms that I think do what you're looking for, such as Wildfire, but that's pretty darn expensive.
You might try setting up an automation service such as IFTTT to automatically add your social posts to a spreadsheet - archiving every single tweet for example. It wouldn't provide the insights data unfortunately. However, if you are using the Goo.gl URL shortener, you'll be able to see exactly how many clicks your links are receiving.
