Do I have a legal case if I found an insect in my drink at a public restaurant. I have pictures and notified corp. office

Were you injured? If not, then no, as a practical matter, you have no legal case--no damages or injury, nothing to sue about. That doesn't mean you can't--as you have--contact the corporate office and see if they will compensate you in some fashion; but there is nothing to sue about.

(Also, note that just having an insect in a drink does not, even if there was injury, automatically create liability. There must be fault, which means that there would need to be evidence that the insect did not get into the drink after it was served, in some fashion that was not he restaurant's fault.)