No. Bed bugs are also pests in poultry operations, and they're known to parasitize bats. Some labs that study bed bugs rear them on guinea pigs and mice. The bugs might feed on cats and dogs. Fur is probably a barrier to them, but they could feed at any place on the body without fur. Bed bugs are not specific to humans, but they are adapted to parasitizing us.
Some of the dusts that are available to consumers, such as diatomaceous earth, can help in this regard. Pest controllers will put dusts in wall voids and other places where pesticide won't reach. What happens is the bugs will wander through the dust and pick up particles and be more vulnerable to desiccation after that exposure. But dusts will not solve the problem if deployed incorrectly, and if they are applied at too high a level they can cause breathing difficulties in some people.
Bed bugs were mentioned in ancient Greece as early as 400 BC, and were later mentioned by Aristotle. Pliny's Natural History, first published circa AD 77 in Rome, claimed bed bugs had medicinal value in treating ailments such as snake bites and ear infections. (Belief in the medicinal use of bed bugs persisted until at least the 18th century, when Guettard recommended their use in the treatment of hysteria.)
The first question I would ask that person is, what makes you think you have bed bugs? A skin reaction alone does not necessarily indicate the presence of bed bugs. Other bugs, allergies and irritants in the environment can produce similar skin reactions. And it's hard to confidently identify a bed bug bite because reactions vary from person to person. My next question would be, have you seen an insect in an area where you sleep and, if so, was it the correct size and shape to be a bed bug? Carpet beetles in an immature stage are commonly mistaken for bed bugs. The carpet beetle actually doesn't look anything like a bed bug, but it is the right size. And it's another common insect to have indoors around the bed. If you find an insect that you think is a bed bug, save it in a pill bottle or another container so its key characteristics won't get crushed and a professional can identify it.
The size of bed bug bites varies with a number of different factors. Bed bugs inject an anti-coagulant along with their saliva when they pierce the skin to take a blood meal. This anti-coagulant is mostly responsible for how a person reacts to the bite and determines the size of the bug’s bite. Since people will have various sensitivities to the bed bug’s bite, the size of the bite will vary, as well. Another factor that influences the size of a bed bug reaction is the number of times a person is bitten. Bite reactions of people bitten many times are also variable, and their response may be either more or less intense as the number of bites increases.