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Welcome to just answer.
I am sorry to hear about your discomfort,
Though this is not a common symptom but its onset immediately after the procedure suggests that the two are causally related.
It can happen due to debris of a microscopic nature settling in the back of the throat after dental work thereby irritating the throat.
I would recommend that you wait two or three days to see if the symptoms do not resolve on its own, unless the pain is severe. If the pain does not go away, you should probably go back to your dentist once to get yourself evaluated.
As for now, you can take Tylenol (acetaminophen) 1000mg and switch it ibuprofen (2 tablets of Advil) alternatively after every 4 hours. This is a good analgesic combination which will provide you relief.
Following other remedies will also help you:
Start gargling with salt water, ½ tsp mixed with 8 oz warm water every few hours or as needed.
Drink plenty of fluids but avoid juices (they might irritate the throat).
You can also mix a cup of warm water, 2 tsp of honey and the lemon juice (1 lemon) and sip.
I hope this answers your question. Please feel free to contact me again for more information or if you have any further queries or questions that i have not addressed.
I wish you a speedy recovery!