I have actually been feeling the same symptoms.
When I first switched from a droid to an iPhone 6 back in March '15, I started to feel these same symptoms along with headaches and straining my eyes. Was ready to return it, but then I did what everyone here mentioned as far as turning on "Reduce Motion" (along with a few other things) and it helped immediately and I was able to keep my iPhone.
Last Saturday, I updated to IOS 9 and the symptoms came back. Not nearly as bad, but this time I just feel dizzy all the time. So I don't know if its the actual phone, or me.
Thoughts?