Get a geiger counter and check the water and milk yourself before you use it. A true geiger counter, not a "radiation monitor." The scale on those is set too high to be of use for lower-level contamination.

Everything will not be contaminated at the same time.

Most bottled water is just local tap water - it hasn't been on the shelf very long, so it won't be uncontaminated very much longer.

Spring water and water from a well will be ok a little longer, but eventually it will be contaminated [to a lesser extent] as well... In fact it may be contaminated later and longer than regular tap water, depending on depth and rainfall at the source, etc.

Time is the best antidote. The longer the time from contamination with radioactive elements, the safer it will be, so have a couple of week's stock on hand, that you already know is safe - otherwise you'll have little choice but to drink questionable water.

Fallout will persist for a couple of weeks after they seal those POS leaking reactors. It will persist in the environment for a few months - but some places will not be contaminated as much. Once folk figure that out they will try to get their food/water/milk, etc from there - prices will spike, and nasty, unscrupulous folk will sell contaminated food to the unsuspecting.

Don't count on your government to tell you what is going on.