Like you, I am a newly diagnosed apnea patient. My first study was done using pillows, and it went well. The technician had about 30 different sizes. When I went to actually pick up the mask, though, I had only three size choices: Small, Medium, and Large. Now, I have been gifted with an odd sized nose such that one side needs a medium, the other, a large. My DME didnt carry such a mask. I found here that such masks do exist: The Puritan Bennett ADAM nasal pillows allow for a separately sized nasal pillow for each side. That is a mask I am currently looking in to.
Currently I am using a ComfortGel Nasal Mask from Respironics. It does not fit me well; I have two scabs on my nose because of it. At night, I put a band-aid over the scabs, and thankfully, they are healing well.
Other masks available are the full face mask (FFM), Hybrid (nasal pillows with interface covering your mouth), and there is an oral mask out there for those that breathe through their mouth only. If I could get Nasal pillows to fit, they would be my first choice. Why? With Nasal pillows on I can read. I cannot do that with a nasal mask. I suggest that you go back to the place that gave you your first mask, let them know of your difficulties, and ask for options.