It sounds like a classic case of shipping sickness to me...and trust me the heifers will get it to.
When we move animals, whether it be from 10 feet from one stall to the next, or 1000 miles to a new home in a new state, the move causes some level of stress in the animal. Seasoned show animals who are used to going up and down the road a lot dont stress as much, but a younger calf that hasnt been hauled much gets stressed out more by the move. We especially see this in animals that are young and being transported to a new home or location for the very first time.
Stress weakens the immune system making the animal more suseptable to pathogens like fungus, bacteria, and viruses! The most common of these pathogens,and the ones most likely to strike during these short perios of stress induced immune defficiencies are those involved with resperitory infections. Thus you are seeing the runny nose, basically the same as a common cold, and your new guy is just plain feeling yucky and doesnt want to eat. Pretty much like any child who has a bad cold.
There are several antibiotics out there that target bacteria in the respiratory tract but I ussually use something common like LA 200 etc. I would also recomend adding an electrolyte like Bounce Back to his water...we use it all the time in our horses, bucking stock, show calves, cow herd, hogs, goats, dogs its great for helping them get back on track more quickly after they have been stressed by things like heat and illness!
DISCLAIMER I am not a vet(though I have spent several years working as a Vet Tech), I am not licensed to diagnose illnesses in animals nor prescribe treatments. I am simply hearing the symptoms and giving my opinion on the most common illness with said symptoms and onset. So please dont take what I said for fact on your animal...I have after all never seen the animal in question. :
