No, you are not. This grep command will only match lines that contain the exact string ~Y or YES~. If you want to match any line that contains ~Y, ~y, YES~, YEs~, YeS~, Yes~, yES~, yEs~, yeS~, or yes~ you need something much more like what protocomm suggested (but for EREs with alternation, you need egrep instead of grep).

Please describe in English exactly what you are hoping to match with your grep commands. Note also since you apparently aren't matching complete fields, your search for NO will also match the lines containing No Resonse. I.e., the lines containing ~NO~ and the lines containing ~No Response~ will both be counted as matching ~NO when doing case insensitive matches. Is that really what you want?