Had laryngitis w/low fever have intermittent coughing attacks, even with cough medicine (benzonatate). Been gargling w/salt water etc. Next step?

Throat scope. Chronic cough is either lung, sinus/nasal, or stomach acid reflux. A lighted scope, etiher nasal or oral, could be very helpful.
Ibuprofen. Drink lots of fluids and take Ibuprofen or tylenol (acetaminophen).
See doctor... You need to see your doctor to diagnose these symptoms, especially if you have ever smoked. These symptoms can be due to benign conditions like viral infection resulting in inflammation of this part of your airway but there are malignancies that can result in the symptoms you describe. See your doctor to be certain of the diagnosis so treatment can be given. If you are smoking, you need to quit!