Problem installing package rbp2-image-4.3.3-3-osmc

Your card is probably fine but appears to be affected by the sdhost compatibility issue discussed here. This has resulted in file system corruption and your /boot partition going read only.

Please try a fresh install of the November release and then updating - this will take you to the December release with the 4.3.3-3-osmc kernel, which should work fine for you. (4.3.3-1-osmc and 4.3.3-2-osmc are the problematic kernels for you)

Your problem is not with 4.3.3-3-osmc, but with the previous kernel you were running during the upgrade to 4.3.3-3-osmc having issues with the SD card thus causing corruption.

There is likely too much file system corruption for the system to be salvageable without a fresh install, even if it does appear to be booting.

Please also post the exact make and model of your SD card.