You cannot fsck a mounted fs. And you cannot umount /home.
So probably do (from heart, so please cross check):
dd if=/dev/mmcblk0p3 of=/home/user/MyDocs/p3.img
fsck /home/user/MyDocs/p3.img

If some error pop up, you may correct them on the img file. But to correct them on device you would need to bring it back to /dev/mmcblk0p3. I am unsure if
dd of=/dev/mmcblk0p3 if=/home/user/MyDocs/p3.img
would work..
Maybe better try that with a Linux system and all partitions mounted to that PC (e.g. via ubiboot. Or are there other rescue systems?).