Tapers are always talking about drugs....
A decongestant like Pseudoephedrine (generic Sudafed) might well dry you up.
An antihistamine/anti-allergy drug like Zyrtec or Claritin might also help. Look at the active ingredients; there are generic equivalents to both probably right next to them on the shelf, like Wal-Zyr and Wal-itin at Walgreens. Try a small sample of each to see if it works for you before buying a whole bottle.
There are also combos like Claritin-D (D for decongestant = pseudoephedrine) but you'd probably pay more for them than for taking two pills. And if pseudoephedrine works by itself, all the better.
Benadryl will make you woozy, as will some other antihistamines and cough syrups. The ones above won't.
All of them are over-the-counter, though you will have to show ID to buy the pseudoephedrine because apparently it is used in meth labs.