How to repair towel rack that was anchored in drywall
I would use a jab saw to enlarge the hole. Then use a rod of wood and place it behind the spot your towel rack will eventually sit. (Make sure the piece of wood is longer than the towel rack bracket). Screw through the drywall above where the towel rack bracket will sit and below it. This will anchor the wood to the back of the wall while you patch the hole. Once that is done you can patch the hole with a pathig kit (ex.  https://www.amazon.com/Wall-Doctor-Drywall-Patch-2)

Once you have let that set and cure you can remount your towel rack bracket. U can remove the extra screws and patch those holes over with a little spackling.