If this does not work, and you still can't get it updated. You can as mentioned by @neilth reach out to your carrier directly to see what options are available. They can also confirm if your device is completely up to date based on what model you have.
If you've tried going through the carrier, and that was of no help, It's possible your device may need a reflash. I would recommend reaching out to a local Samsung experience shop or UbreakiFix, you also have the option to call 1-800-726-7864 to see about getting service set up for your device.
(Please know if you have to do the reflash, and call in for the service. Once the device is shipped in, due to you having the broken screen, they will probably request that the screen be fixed prior to updating the device. As physical damage can be the cause of many, many, symptoms with your device not working or functioning like normal.)
