I think you may have steroid rosacea. Desonide is a weak steroid but it can keep rosacea coming back as soon as you stop it. My advice would be to continue the doxycycline. It would be best to stop the desonide.. The flareup will go away soon. benzoyl peroxide isn't harmful but it's not that important either if you're on doxycycline. Then you can see a dermatologist when you get back to the States if the rash is still there. You will clear up, though, don't worry.
Best.
Dr. Rockoff