Wait a second.
You have a right to eat your burger with two hands, except when you’ve eaten most of it and are down to a small piece. Then it looks like a mouse chomping on a piece of cheese.
My concern is that if you are to the point of being both sick and tired of being told your behavior is not ladylike, how many times are you being told this? Is it the same person or numerous individuals?
Also, if so many people are telling you this, think about the rest of us who notice it and are not saying anything. For every person who tells you this, there could be ten out there who noticed, but said nothing.
I suggest compromising with the world. Maybe try using a knife and fork with your burger. BUT..after cutting a small piece of burger place the knife down, switch the fork back to the other hand, and then prong and eat.
Chewing is whole other story.