An interesting thing with ibuprofen is that at the regular dose of 400mg it inhibits pain but if you take 1600mg it doesn't inhibit much more pain than the 400mg dose, but the inflammatory effect does increase significantly. A lot of people don't know that and take too much thinking it scales linearly.
And when you want to be gentle, you alternate between them.
So don't be the "smarter" person. Do as your doctor says and if you have doubts, consult another doctor before just doing what you think is safe, but actually isn't.
In general, taking a lower dose than recommended can cause problems, but aside from antibiotics, the problems are probably going to be from insufficiently treating the underlying condition, rather than the medication itself. Most OTC drugs give a single recommended dosage for all adults, so some people will necessarily get a lower "effective" dose than others (eg. a 200 lb man compared to a 90 lb woman).
> Specifically, the two mentioned in the article. [...] but if my doctor tells me to take 1 ibuprofen every 6 hours or so, if I halve that am I actually doing more damage?
With the caveat that I'm not a doctor, you should be fine: the only effect of acetaminophen is pain suppression, so if the pain is tolerable, then you should be fine. Ibuprofen has some anti-inflammatory effects that could be important here, but realistically, if the anti-inflammatory effects are the primary reason for the prescription, then your doctor is more likely to prescribe naproxen or celecoxib.
But if this ever comes up for you again, probably the best solution would be to tell your doctor/pharmacist "I have a high pain tolerance, would it be okay if I take less?", since in my experience, medical practitioners are generally pretty happy to hear when you want to take less drugs.