I have a blister on the back right side of my throat. I haven't had any sexual relations with anyone and haven't kissed recently. What is it?

Throat blister. It is difficult to guess what this could be and an evaluation of the blister, adiscussion with you about its timing of onset and severity, and more about your medical history is needed to suggest diagnoses. Mouth blisters commonly occur as a result of infection (sexually transmitted or otherwise), irritant/allergen exposure, medications, stress, and rarely from systemic diseases such as Lupus.
Difficult... It is difficult to tell what it is without taking a look at it and not knowing what oner symptoms/history are related. Most of the time this could be caused by a virus and if this is the case should go away in a few days. If it persists see your doctor for formal evaluation.