I have sleep apnea and you should be aware that as already said that a prescription is needed for both the machine and mask. These can be very expensive without insurance, say in the $800 to $1,000 range. Because of the risk of bacterial growth in these machine I would be concerned about a used machine unless you know how to clean.
Then there is the question of the setting for the pressure. The machine maintains a positive airway pressure. This is used to "blow open" (my words) the air passage. To low and the airway is not open, to high and it is uncomfortable.
There is a simple test that can be run with a recording pulse/oxygen meter that can trace the level of oxygen in the blood during the night. If the oxygen level is high through out the night a CPAP machine may not needed (only a doctor can say for sure), if it gets low then this could given your doctor to insight to have further testing.
I personally do not agree with Doctor shopping, but, if you do not have faith in your Doctor look for another.