Hi Gammaw,
The desk does have two towers and you can put your nebulizer in the other drawer. I'm including a link for you so you can click on the little pictures to see all the details of the desk:
http://www.ikea.com/ca/en/catalog/products/60245721/You will see that there is a hole in the left tower where the cords come out. (Which is where my Respirtech cord comes out. You can also see in my picture that my vest is stored on the top shelf, and I've just got the hoses loosely jumbled in there with it. Since I've got a respirtech, taking off the hoses is a quick and easy operation both from the compressor and the vest. But if you have a Hill-Rom, you could, I think, store the compressor in there with the hoses attached. There looks to be enough room, but like I say, it's best to try before you buy the desk. By the way, the shelf in the left can be moved up and down, so there is a fair bit of flexibility.
I do use a nebulizer, and the Devilbliss Pulmoade nebulizer compressor fits very well in the right-hand drawer. You just need to take off the power cord when you want to close the filing cabinet door. The top drawer above the file drawer has room to store hypertonic saline and another drawer inset for your pencils and stuff. If like the original poster, are looking for something that is a hutch, Ikea makes a top unit for this desk that gives you more nooks and crannies. Here's the desk with the top unit:
http://www.ikea.com/ca/en/catalog/products/S09000500/ Those drawers in the top part might make good storage for meds.
There is another unit might work as a vest/nebulizer storage solution too. It has a smaller profile, but
must be fastened to the wall:
http://www.ikea.com/ca/en/catalog/products/10245709/ If it isn't fastened to the wall it could topple. Also, you can get that one with an add-on unit too for extra storage:
http://www.ikea.com/ca/en/catalog/products/S49932830/
If you're looking at these and thinking they don't match your decor...just google "Ikea hacks" and you'll come up with thousands of images of ways people have made furniture fit their purposes and their decor. Lots of inspiration to store the stuff you need and have it look beautiful and function well. Their casters, drawer slides, etc. rock. Every Ikea store also has an "as is" section of returns. If you're on a budget, take a look there and see if there is something that might work (especially after you've taken a look at some other Ikea hacks). There are some truly beautiful "hacks" out there by architects, who have made these humble pieces gorgeous. Just remember when you put them together, to work on a soft surface, such as a blanket. Pine is soft and scratches.