Yup, perfect answer .... nothing else to add besides the fact that peak flows aren't always the best way to determine an attack.
Peak flows are only useful when compared to YOUR personal best, not the "average" numbers. So I agree that you need to track the numbers while you are feeling good to see how they drop during an attack.
Normal for me is around 500, but the "average" peak flow for my weight/height/age is 440, so when I did my first pulmonary function test and blew a 320, I was considered normal (ventolin only increase it 12%), but with air trapping. Attacks are different for everyone, my are very symptom based and don't show dramatic drops and raises. I will slowly drop from the 500 to 350-380 with a decrease in the efficenness of my ventolin/atrovent. Eventually the inhaler does nothing and I feel like crap. However, most of the time when I get to this point, a neb and doctor visit does not increase the peak flow at all, even with 50mg of pred it takes days for the peak flow to increase.
So by recording your numbers over time, you will get to know how your lungs and peak flow values correspond to symptoms and attacks.
I, too, am an asthmatic and have a nebulizer machine at home. I was diagnosed with my asthma at age 18 (I'm now 47), and "back then", it wasn't as common to have a neb machine at home unless your asthma was not very well controlled (mine wasn't). However, I do believe nowadays it is much more common for asthmatics to have one at their home - and it makes sense to me - having one can definitely help avoid trips to the ER (which end up being much more costly for both the patient and the insurance company). However, not all asthmatics have them.
Of course, not all asthmatics are alike, the same as all pain patients are not alike, the same as all people in general are not alike. So, while one asthmatic may need to use their nebulizer 2-3 times a week, another one may not need to use it more than once every other month. I feel, also - although I'm not a doctor - that some of it depends on what other meds you are on for your asthma and how well THEY are controlling your symptoms.
Do you also have a "rescue" inhaler to use when an attack strikes or are you only using the nebulizer for the attacks? Are you on any preventative inhalers or oral meds? I, myself, have a rescue inhaler that is my first line of defense and then if that doesn't help, I go to the nebulizer. I'm not currently on a prevenative inhaler as I've had reactions to several of them. My prescription for my nebulizer is written that I can use it every four hours if needed, however, I first try my rescue inhaler and if that doesn't provide relief, then I go to the nebulizer. I've learned throughout the years, how I feel when an attack is coming on, so therefore I can sometimes "head it off" with the rescue inhaler and not have to use my neb. However, during weather changes, changes of season, extremely heat and humidity, or when I'm sick, I do have to use the neb much more often - sometimes several times a day. I've also learned, though, too that when I find myself having to use it more than 3-4 times a day (keeping in mind that my script is written that I could use it up to 6 times a day), then it's time for me to hit the doctor's office and get a round of steroids.
Yes, it is possible to have an asthma attack with cough being the main symptom, although the wheeze is what most doctors listen for first still.
One thing I do want to mention, though, is that if you are coughing up colored sputum, what you are experiencing may not be an asthma attack at all - it more than likely is an infection. Whenever you have colored sputum, that is a sign of infection - the sputum that you cough up during or after an asthma attack is usually clear to slightly white. So that could also be a reason why you're not wheezing during these attacks - rather than actual asthma causing them, it is the infection causing tightness adn irritation to your airways. Unfortunately, asthmatics are more prone to respiratory infections such as bronchitis and pneumonia and sometimes even the meds we have to take/use can make us even more prone yet.
Have you seen a pulmonologist and had a PFT (pulmonary function test) done? If you haven't, you should. It's a simple test where they have you do several different breathing tests to see what your peaks/abilities are both before and after administration of a rescue type inhaler. This helps give them a good baseline for your breathing that they can use to compare when you're having trouble. While the peak flow does a similar thing, unless you are using the peak flow more than only when you are having trouble, you don't get your baseline numbers to be able to know when YOUR numbers are low. Basically, even if you're getting higher numbers on the peak flow even when you're having difficulty, if those numbers are much lower than what your NORMAL good day numbers are, then that's a sign of a problem. Do you have a peak flow at home? Do you track your numbers even when you're having good days?
To me, it sounds like your breathing problems are not adequately controlled, so I would definitely consider being seen by a pulmonary doc.
Best of luck!