Every amateur mechanic has undertightened a square taper crank at some point. In my experience (yes, I did it too...) once you feel it loose the arm is ruined and needs to be replaced. It only takes a little movement to ruin the tapers. Your best bet now is to re-install it with as much force as you possibly can and start shopping for a new crankset.
For a much better and detailed explanation, see here:
Installing Cranks by Jobst Brandt
Originally Posted by
bikemig
I ran into a bike mechanic on a tour who told me that square taper cranksets are prone to failure. I don't think that's true but it's clear that a lot of people tighten them down properly.
That mechanic was wrong, but lots of cranks do get ruined from undertightening. Installed properly, a square taper crank will be good forever or until the bottom bracket needs servicing/replacement.