If you take your problem to management, you need to haul along with it the solution for that problem, and the justification.
The key to this sentence, is the justification.
You need to show, likely with dollars and cents, how much productivity is being lost because the current staff is being pulled away to deal with general IT issues. Lost productivity for the end user. Lost productivity for you, which in turn means delays and more lost productivity of other projects.
Bringing in your solution (additional staff), will keep you productive with your main focus. It will get quicker responses for general users thereby boosting their productivity, and so on and so forth.
In business, it's all about the bottom line in many respects. Something that costs you X to implement, but makes you 2X or 3X or 4X in return is an easy decision to make from the business perspective.