I feel you are doing more damage than repairing, I am afraid. Scratched tile surface is not easy to repair and probably needs to be replaced eventually. When using the diamond blade you just move the blade backwards and no need to push it back and fro. Just my two cents.
Hi, Kylie. I'm currently using this FILA Grout Sealer. I can't claim it's the best, but it seems to work for a while. Just keep in mind that you need to scrub the grout and stones regularly and then re-apply the sealer every month or so. www.homedepot.com/p/Fila-Grout-Proof-24-oz-Tile-and-Stone-Sealer-44750612AME/206392674