You seem to have misunderstood a lot of things.
There are 3 types of painkillers and only one of them have effects on memory. None of them interact with the adenosine receptors.
NSAIDs(eg. aspirin, ibuprofen) work by inhibiting the cyclooxygenase-2(COX-2) enzyme which is responsible for inflammation.
Opioids work by activating μ-opioid receptors. This also causes the brain(and other parts of the nervous system) to slow down, which is why it effects memory.
There’s also paracetamol, but how it works as isn’t fully known yet.
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