Ekbom syndrome or delusory parasitosis.
I've actually attended a lecture on this subject delivered by a psychiatrist believe it or not!
All sorts of theories offered during the lecture. Personally, I think it's down to a combination of two effects. The skin is our largest and in some ways most complex organ. It has billions of sensory cells sending a constant stream of data to our brain. To prevent overload the brain ignores most of these signals unless they are unusual - which is why most of the time we don't/can't feel the clothes that wear. Every now and then we get a sensory challenge. Insect bites are a good example. We then subconsciously worry about getting bit again which means that the threshhold at which the brain registers data from the skin is lowered so we 'feel' more. Any slight sensory challenge [including heat (and especially prickly heat), salty sweat or minute scratches, infected hair folicles, blocked pores, and even individual hairs moving on the skin etc] is then detected by the skin that we would otherwise not notice leading to the sensation of phantom stings.
There are other possible causes. Some serious conditions can cause sensations akin to phantom bites including diabetes, certain cancers and certain other diseases such as gout also affect sensory perception in skin.
It's amazing how deceptive the sensations from the skin can be and it's actually quite difficult to tell the difference between hot and cold and pain. We were shown quite an interesting experiment. The presenter had a hot glowing ember in a fire. A volunteer was blind folded and informed by the presenter that the hot ember would be placed on the palm of their hand and they were to let the presenter know if the ember was too hot. Un be known to the volunteer the presenter also had a hidden ice cube which they placed in the volunteer's hand instead. The reaction was quite something with the volunteer screaming from the apparent scald they received. Tried it a few times at barbecues after that - neat little party trick - he, he, he!