Yes you have used the idiom correctly. I've copied and pasted this explanation from the idioms linked to this website. A lot of idioms are all explained by clicking on the link. I use a lot of different idioms with my students by getting them to make up sentences to ensure that they are using them correctly (like in the way you've done).
Up to the eyes
You are up to your eyes in something, you are deeply involved or to have too much of something like work/homework. ('Up to the neck', 'up to the eyeballs' and 'up to the ears' are also used.)
In the UK we tend to use 'up to my eyes in work' or 'up to my neck in work'.
Hope that this helps and you don't have too much work to get through!
Student or Learner