Besides answering medical questions, I am also a breeder of White West Highland Terriers and have one rescued female that takes prednisone on occasion due to allergies.
Is the name of the medication you took possibly called Temaril-P?
Routinely, medications we humans use on a regular basis are also prescribed to dogs and other animals. The composition is often the same; however, the pills are formulated in doses appropriate to animals. For this reason, the dosing parameters may or may not be adequate between humans and dogs.
It is never recommended to take any medications that have not specifically prescribed to you by your physician. Additionally, it is even more important never to take any medication that is label for use in animals only.
Let me know precisely what the label information off the dog's prescription bottle is. My concern, is that they may or may not be straight prednisone. Often, prednisolone and other medication is combined in some of these canine prescriptions. They are manufactured to be canine specificm, as some medication combinations used to multi-symptomatic conditions in dogs, for example cough and itching.
I will check back with you as I need to know precisely what the label says. Prednisone is a term loosely used by the vet as most owners know what this medication is, but it may or may not soley contain prednisone only as it was prescribed for canine use.
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Corticosteroids (Steroids, Adrenocorticosteroids, Adrenocortical Hormones)