Bad sprain? I could get you a painkiller (7)

I believe the answer is:

aspirin

I'm a little stuck... Click here to teach me more about this clue!

'painkiller' is the definition.
(I know that aspirin is a type of painkiller)

'bad sprain? i' is the wordplay.
'bad' indicates an anagram.
'sprain'+'i'='spraini'
'spraini' with letters rearranged gives 'ASPIRIN'.

'could get you a' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for aspirin that I've seen before include "Common drug in Paris" , "Analgesic compound" , "Headache pill" , "Commonly used pain-killer" , "number" .)

I've seen this clue in The Telegraph.

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