Looks right to me.
Some suggestions:
-always carry the units through correctly to make sure you are doing it right; I think the first step you did missed the N/m
-you probably don't need to convert everything to N and use *10^6 everywhere; it saves some time and probably less mistakes just to leave the M in there to the end;
-a shortcut here is to just divide the distributed load by the width since a distributed load is sort of like the stress already in one dimension