Welcome to the forum, EF.
Sorry you had such a bad reaction. Cymbalta works by raising serotonin. You may have had a serotonin reaction (serotonin syndrome). The feeling hot and red skin are typical. It's serious and you'll have to be very careful from now on with ANY meds that raise serotonin.
Were you taking any other meds at that time? I can get SS (serotonin syndrome) from taking tramadol and Flexeril even on the same day.
Talk to your doctor about this! He may not believe you because it's unusual. SS is however, listed on all the drug websites for Cymbalta.
There is a treatment for SS you could have on hand for the next time. Get the doc to prescribe a benzodiazipine. I just take 1 Valium (diazepam 2 mg) and it usually stops quickly, although I may need another after a few hours. Valium isn't very toxic. Or, you can go to the nearest emergency room and tell them you are having a serotonin syndrome reaction.
Next time it happens you could get a night's sleep.
Now that you've read that, note that I am NOT a doctor. Also note I said to talk to your doctor about this.