Shower drain

I have used Drano a time or two. I just make sure there is water in the grey tank to lessen any effect it may have on the drain seals. After the shower drain runs good, I dump the grey holding tank.

You might try the vinegar and baking soda trick. Here's one source: http://www.crunchybetty.com/clean-your-drains-with-baking-soda-and-vinegar-surprise
One of these days I'll learn how to hyperlink...
I'm thinking you didn't get all the hair out of the drain. Don't know that tool you bought but there are some about 3 feet long that should get it all. One kind has `velcro' on the end and others have barbs along the length. I get them from Ace hardware.

Bad for the seals in the drain valve
Try boiling water then repeat