Its never a good idea to toss in a brand new purchased animal in with established animals for many reasons.
First reason: spread of pathogens/diseases/parasites etc. Even a healthy looking animal can be carrying or sick with some disease or have internal or external parasites.
Second reason: The stress of traveling and being introduced to a new environment is bad enough for animals, but putting them into the territory of other animals just makes it more stressful.
Third reason: compatibility. Even social animals don't always get along and Bearded dragons are not all that social. They do interact in the wild but almost only during mating season and to indicate who is the most dominant in any given territory. In captivity some females and male/female groups can get along for years, till for some reason one turns on the other and serious injures, maybe even death of one or both involved can result.
Forth Reason: food/basking spot/etc. competition/dominance issues. If one dragon takes charge, he/she can easily prevent the other from accessing the better basking areas or getting their share of food.
Fifth reason: Cage size....though this isn't really a reason to quarentee animals but if you don't have a large enough cage to house more than one animal...it increases stress levels for all occupants of the cage. Remember the minimum recommended cage size for a single adult dragon is 4'x2' of floor space with 18-24 inches of height. For two dragons, the cage should be larger, 5'x2' is a good start, or even 4'x3'. 5'x3' is a great size for a trio of dragons. these larger cages should also have multiple basking areas etc as well.
For dragons, the minimum recommended quarantine time is one month...most recommend three months, with at least two clean fecals taken during that time, or even once a month. A vet inspection should occur as well to make sure the animal is healthy in all aspects. Animals may look healthy but since they often hide symptoms due to the fact in the wild, sickly animals are preyed upon above healthy animals.
Now onto your problem. It sounds like your new dragon has an Upper Respiratory Infection...this should be brought to the attention of a vet immediately. At the very least, separate him and put him into his own cage with appropriate heating and lighting and observe for 24 hours. If he gets worse, go to the vet, if he acts normally, continue to monitor..but if he refuses to eat etc...vet visit is still required.
Contacting the vendor you bought the dragon from should be done right after booking a vet appointment, or at least within 24 hours from when you bought the dragon. Most vendors will work with you for either an exchange or refund...but most won't do it after a certain amount of time goes by (like 24 hours).
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PHLdyPayne