TLDR: its just his preseminal fraction's cleansing action reacting with human esophageal tissue. If you're a normal healthy adult with functional immune system, you'll get a dry raspy throat like the rest of us for an hour afterwards, then it clears on its own, as you've seen. Its routine. All part of the experience. We bear and wear it proudly, like the secret badge of pride in accomplishment that it is!
Longer version: what Nekdoneco and Pes have said. We've covered the topic before, its nothing new, and generally nothing to worry about. My own theory goes something along the lines of this being a reaction specifically to the cleansing action of the male's preseminal fraction. Dogs are known to ejaculate in three distinct fractions: pre-seminal | seminal | post-seminal. The preseminal flushes / cleanses the urethra of the male and does the same for the vaginal canal of the female, preparing it for live sperm so that the cells won't die of conditions in these tracts. Whatever it does there, it also tries to do in our throats, but our throats don't like it and respond with mild inflammation. So, nearly all of us humans get a transient condition after the fellatio act, "presenting" with no other symptoms than that which could be described as a dry, raspy, itchy or mildly 'sore' throat for an hour or few after the act of swallowing dog semen. Then it clears on its own. No swelling, no trouble breathing or swallowing, just a uniquely dry, raspy throat for an hour with no other symptoms. It should feel similar to -- but not exactly the same as -- a sore throat associated with common cold. Do the allergy tests as described on trivial parts of your body and mucous membranes, but you'll probably be fine like the rest of us. Happy sucking!