I'm thinking this post might belong in Student's Corner, but anyway...
8 out of 9 people are right-handed. Most right-handers aren't terribly good with their left hands, it's a corpus callosum thing, the connector between the two hemispheres, also a practice thing. The world, including scissors, writing, locks, and many other things, is built for righties. Lefties have to learn to cope with these right-handed conventions and, consequently, develop their right hands better than righties do their lefts. Also, their corpus callosi are built a bit differently. Whew!
Anyhow, playing piano, even if your left hand is stiff, is a good thing for you. Keep doing it. It's making your brain do new and amazing things. Of course, relax, relax...you're probably getting tight because you're not used to using that hand much.
Many piano parts have skips and jumps in the left hand, fine work in the right. In time your left hand will rise to the challenge. If you despair, remember the story of Wittgenstein, who lost his right arm in WWI and got Maurice Ravel to write him a concerto...the resulting work remains a mainstay of the repertoire and doesn't require a thing from the other appendage.
Here's to the left hand! Misnamed el mano sinistero, I might add.