Tried sleeping pills yesterday... Add them to the pile of drugs I'm immune to.
What kind? Because there's tons of different sedatives - you're not going to be immune to all of them.
Melatonin? But I am also immune to all painkillers I've tried, cough medicine, and basically everything else I've tried...
Melatonin's weaksauce, and - once again - it depends on the type of painkiller, the dosage, and maybe even the type of pain. With cough syrup, it depends on the type even more: Either you get an opiate-like effect (codeine-based cough syrup, quite rare), or a dissociative effect (DXM-based cough syrup, quite common), or few/none at all (other antitussives, homeopathic 'medicine').
In any case, an outright immunity is practically impossible, since that would mean that your fundamental biological processes differ vastly from those of the rest of us. It might be that your enzymes responsible for getting rid of such substances have higher activity, or that your guts absorb these medicines at a lower rate.
To get a definite result, you'd have to experiment with known dosages of known substances and different routes of administration, like subcutaneous, intramuscular or intravenous injection, sublingual administration, rectal administration, smoking the stuff... Most of these bypass the liver to some degree, giving some indication of where the substances are held up.