One of two things: Either the extractor rod unscrewed a little under recoil, and now it is jammed against the front of the extractor rod cutout under the barrel, preventing any movement of the cylinder; or, a few granules of unburned gunpowder became trapped under the extractor star during ejection of the last cylinder of empty cases, and when you reloaded and closed the cylinder, the granules kept the extractor from fully seating into its cutout in the rear face of the cylinder, making the cylinder effectively too long, and it is now binding so severely in the frame's cylinder window that it cannot revolve or be opened.
Note: all the following MUST be done with the weapon pointing in a safe direction; safe enough that if the gun were to accidentally fire, no one would be injured or killed, and property damage would be minimal. NEVER point it at any part of your body during handling, of course.
For the first problem, try using a tiny screwdriver to push the small spring-loaded locking bolt (at the front of the extractor rod) forward, which may release tension on the cylinder enough to get it open using the thumbpiece (if you can see any part of the bevel on the end, try to work the blade in far enough to press on this angled area). If that doesn't work, try pressing inward on the left-rear edge of the cylinder with your left hand, like you are trying to close it into the frame, and at the same time, use your right hand to press the thumbpiece forward to release the cylinder from the frame. If you can get the cylinder to unlock using the thumbpiece, it then should be possible to roll it out and unload it. Alternatively, keep pressing forward on the thumbpiece while alternating between pushing in (closing motion) on the cylinder, and pushing out (opening it) to get it to wiggle free.
Second-to-last resort: If you know how to completely disassemble a S&W revolver, you could remove all the internal frame parts, and then use a soft metal rod or punch to tap the center pin out of the recoil shield to unlock/open the cylinder.
Last resort: take to local gunsmith (transport VERY carefully if still loaded), tell him what happened, and let him take it from there. Be prepared to spend $50 (minimum; likely more, maybe MUCH more) for diagnosis and correction of the problem, and an overall inspection for bent/broken parts once he gets it open.
"Placement is power" -- seen in an article by Stephen A. Camp
(RIP, Mr. Camp; you will be remembered, and missed)