I had this one morning. Just happened. My eyes were stinging, my ears ached real frikin bad! I felt like vomiting real bad, but didn't. I saw boxing trainer about it, he told me that because it was warm in my house, and I stepped out into the cold and started running, the cold air pressure passed (and went in) my ears faster. He told me that if the air temp in your house is a big difference to outside when you run, it can cause pain and discomfort because of a sudden change in body temp.
And yeah this caused burning eyes and made me feel like throwin up.

Don't if it is the same as what you suffering but yeah.

To get over it I just sat outside in the cold for like 5 mins and started jogging slowly, building up my pace into a run. This helps your body adjust, and now I wear a beanie too.