In regular expressions, the brackets (( and )) are actually reserved characters so you will need to escape those. So this regex should do the trick: _\\(\"(.*)\"\\). However, you also stated that you wanted to find words which must begin with my( and must end with "). So you will need to add anchors like so: ^my\\([\"'](.*)[\"']\\)$. This should match any string which starts with my(" or my("' and ends with ") or ').
The ^ and $ are anchors. The ^ will instruct the regex engine to start matching from the beginning of the string and the $ will instruct the regex engine to stop matching at the end of the string. If you remove these anchors, the following would be considered as matches: foo my('...') bar, my("...") bar, etc.
This however will make no distinction and will match also strings like my("...') and my('...").