Hello Christina, You could say "get behind with" and it means to be late paying installments for something.So it is not proper for this context. Example: If you GET BEHIND WITH mortgage payments, you might lose your home. If you want to express being in a retarded state concerning your work you could say : " to drop behind in my work"

"I'm behind in my work" is the better way to say this. The two statements mean the same thing, but native English speakers would say "behind in" for most cases. "Behind with" is also said, but it is less common. There is no rule to learn the difference, unfortunately.

"She was behind with (= delayed in) her work for the English course." "The old woman was behind with (= late paying ) the rent." "I'm behind on everything." These sentences from different sources(dictionary and books).Therefore, I think (2)"I'm behind with my work" is a right sentence.

I would say "I'm behind on my work."