Is this rosacea or an allergy? (Photos)

last month I had redness and little bumps Like papules only on my forehead, nose, area around neck and ear and the top of hands. I treated with Fenacea.3 weeks later,stressed at work, today I was out under the sun -night time all the same areas started to itchy and became red,but I can't see any pustules. The first time I saw a Dermato and she said it was an allergy.Could it be rosacea even tho I don't have redness on my cheeks? And if caused by stress/sun, do I still treat it with antibiotics?