We have had years of this from the males in my family. First of all, get an albuterol inhaler. This CAN be cough variant asthma. Even if it isn't, the inhaler will make your lungs work better and every little bit helps.
I would go at this from several different directions. First, the humidifier or a great big pan of water on the stove on low heat. THis will help.
Cough medications are not one size fits all. You need the right medication for the problem. You NEED mucinex. Either splurge for the expensive brand name that will work for 12 hours OR go for the instant relief generic/house brand (active ingredient guifenasin) and take it every 4-6 hours. This is the active ingredient in plain robitussin also, and it is fine to use that if you like that version. Guifenasin will make your mucus not sticky, so it is easier to cough up and it won't feel like it is taking a chunk of lung up with it
next you should consider an antihistamine. Benadryl is actually still the most effective, so if it doesn't knock you out too much then go for it because it is cheap, will help you sleep AND will handle nausea - it is actually almost as effective as phenergan for nausea and more effective than zofran for many people. It is fine to use claritin or zyrtex or allegra or whatever works for you. The antihistamine will help keep your body from making as much new mucus and will dry things up.
A decongestant may be needed (pseudoephedrine is still the best but the OTC stuff labeled PE works for some people) esp if what you are coughing up is very thick. It is common to need an expectorant (guifenasin), an antihistamine and a decongestant with any respiratory infection/problem.
A cough suppressant should be taken at night. If you don't cough or the cough is not bad enough to interfere with work, try not to take it during the day. The cough won't truly go away until all the gunk is out of your lungs, so if you take the cough suppressant all day and all night then you will have the cough a lot longer. The best cough suppressant is still alcohol, so if you drink, add some whiskey to your hot tea with lemon and honey. It truly will help.
If you don't drink alcohol, then go for the dextromethorphan. It is in the Robitussin DM, most medications with DM and in Delsym. Delsym is a slightly different formulation that lasts for 8-12 hours instead of 4-6, so it is helpful at night. robitussin also has a cough gel that lasts about 8 hours and it is most effective for thank you and husband when they get a cough.
Consider a sore throat lozenge. Sometimes the cough is more of a reflex and the medications in sore throat lozenges or spray will numb that area a little bit so it suppresses the reflex just a bit.
Put a hot rice bag or heating pad on your chest if you can stand it. It helps to relax the muscles and keeping your lungs warm really does help.
I know these are a lot of different medications, but try to NOT buy combination medications. Esp pay attention to ones with tylenol in them because you just can't take any extra of that. Also avoid tylenol if you are using whiskey at the same time.
A good thing is that if you buy the house brands it actually is cheaper to get the individual types of medications and take just the ones you need. The initial outlay is more but you only take the medication you need for the symptoms you are having.
I would also start taking prilosec every day. GERD can cause this cough and we have heard this from the allergy doctor, the family care doctor, the lung doctor, the stomach doctor and the pediatrician. It is perfectly safe to take prilosec for 2 weeks and this may help the cough greatly.
I hope this goes away soon! Sleeping propped up or on a recliner is a big help too.
"if you don't drink alcohol"........
well, I certainly don't drink rubbing alcohol. It might put an end to my coughing however. 
