The "meaning of DX" on your camera is no different with prime lenses, FX or DX, than it is with your current 18-55mm DX lens. The field of view (FoV) obtained with your 18-55mm lens is also affected in the exact same way by the size of the DX sensor in your camera as any prime lens will be.
A 35mm DX lens will provide the same field of view on your DX camera as a 35mm FX lens would, which is also the same FoV as what you get with your 18-55mm lens set to 35mm.
A 50mm DX lens will provide the same field of view on your DX camera as a 50mm FX lens would, which is also the same FoV as what you get with your 18-55mm lens set to 50mm.
If your decision is based upon field of view, then any 35mm prime lens you buy will give the same FoV on your D5500 as the FoV you get with your 18-55mm lens set to 35mm and any 50mm lens you buy will give the same FoV on your D5500 as the FoV you get with your 18-55mm lens set to 50mm (within the minor variation of the exact focal length of each lens - some 35mm lenses may actually be 33mm lenses while others may be 37mm lenses or anywhere in between and some 50mm lens may be anywhere from 45-55mm actual focal length).
If your decision is based upon which f/1.8 lens will give you shallower depth of field then the question is a bit more complex. But in general if you're shooting at different distances to get the same framing with both lenses the DoF will be virtually the same. Shooting at 10 feet with a 35mm lens at f/1.8 gives a DoF of 1.77 feet. Shooting at 14.3 feet with a 50mm lens at f/1.8 gives a DoF of 1.76 feet.¹
What will change by shooting further back with the 50mm lens to get the same framing as with the 35mm lens when both lenses are used on your D5500 is the perspective. Things behind your subject will look closer with the 50mm lens shot from about 14 feet away from your subject than they will with the 35mm lens shot from 10 feet away from your subject. To understand why, please see: Why is the background bigger and blurrier in one of these images?
1. In practice the difference in design tolerances and manufacturing tolerances between the two lenses will be greater than the theoretical difference of 0.01 feet (1/8 inch). Are both lenses exactly 35mm and 50mm respectively? Are both apertures exactly f/1.8? Is the difference in shooting distance you are using exactly 1.428571428571429 times further? Probably not.