Robitussin is usually what works for me. If your doctor or urgent care tries to prescribe Tessalon Perles, these don't work worth a crap for anyone I know who has used them!
Hope you get well soon. Not to be too dramatic, but I once had a lingering dry cough so I went to the doctor and it was pneumonia. The cough being dry was the main indicator of that, and they did a chest x-ray to confirm. I was given a prescription and all was good after that!