Having good command of the upper register is VERY important. To say otherwise is to be wrong.
Yes, 95% of what you will see is below high C. Yes, the middle register is more important and is probably what you should spend most of your time on. But you need to be able to at least play what's written on the page. That 5% has some pretty important things in it.
Also, if your range cuts off at ~high B/C/D, you likely have other issues with your playing that need to be addressed.
That said, your health comes first obviously... If something in your chest hurts when you play high notes, you should probably see a doctor...