I think you can and should make an appointment and see a doctor. As near as I can tell, these sound like bites of some sort rather than a rash. The marks that are left over will fade and go away if you leave them alone. The fact that your wife doesn't have these does not rule out bites, since people differ in their sensitivities. But the only way you're going to know for sure is to be seen in person.
Best.
Dr. Rockoff
I forgot to mention that I recently changed address (different city) including bed, I do not have any pets and my wife does not present any of this symptoms.