It sounds like the grout was never sealed.....Get it as clean as you can go to HD buy Tile Labs sealer comes in container with or a brush or without -- would suggest the one without as you will go through at least a few of the ones with the brush... get your self some headphones and stool to sit on and paint the lines for hours -- it has to sit on top and absorb in and will take more than one coat.... Had my bathroom done 15 years ago including a stall shower spent a few days sealing all the grout (literally) and I have never ever had any mold on any grout... floor grout... mop it and it looks like new.... While I say get it as clean as you can you really should replace the grout than seal it you should have no future issues... all can be done easily but with a lot of frustration from being bored and a lot of time.... but I a lot less time than scrubbing every week for years...