What is the relationship between doxycycline and skin rash or sensitivity?

Two possibilities: One can have an allergic reaction to the antibiotic itself and will manifest as a rash all over the body. Doxy can also make you more sensitive to sunlight, so you can get sunburn on the exposed areas.

Photosensitivity: Doxycycline causes an increase skin photosensitivity, increasing the risk for sunburns or skin discoloration with over-exposure when taking this medication.