Why won’t it hold a charge

You should download 3uTools and plug the phone into our PC and run 3uTools with the iPhone on. This will get you a battery life reading, or you can also do the same via the Settings Menu on the iPhone itself.

I personally advise battery replacement when the health is below 80% but I have seen odd behaviour from batteries with a life of less than 90%.

I would definitely say you have a bad battery that needs replacing :)