If your dog is showing possible symptoms of heart failure, you should get a workup including chest x-rays, full blood chemistry, and an echocardiogram as soon as possible. (I actually get chest x-rays before there are any symptoms of heart failure, as this gives a baseline cardiac size which is used for comparison purposes as the heart disease progresses. I get these baseline x-rays when a dog has a grade II or III murmur, before any symptoms, or even for an older dog who doesn't have a murmur.) Chest x-rays are pretty inexpensive. These tests (chest x-rays and echo) will indicate what stage of heart disease is present (this is different from grade of murmur; grade of murmur is really just a clue as it is merely the sound heard when listening with a stethoscope; grade of murmur may or may not correlate with stage of disease). If there are symptoms, he should already be on meds. The blood chemistry is important when starting heart meds as you want to make sure there are no other problems going on with major organs, etc., and then blood chemistry done after starting meds will make sure there are no side effects from medication.
Where do you live? (I think you are in the US.) If there is no cardiologist in your state, I'd look for a board certified internist. This specialist is perfectly able to diagnose and treat heart disease, particularly degenerative valve disease. You can search here:
http://www.acvim.org/websites/acvim/index.php?p=3
Look for "small animal internal medicine."
There may be other specialty clinics in your area.
Chest x-rays are a good tool to use for monitoring increase in heart size, whether or not heart is constricting/pushing against main airway (which can cause a cough even without fluid in the lungs), the presence of fluid in the lungs, etc. Be aware, though, that a GP vet might not be good at interpreting heart size, esp. with a Cavalier which has a somewhat different cardiac profile from many breeds. I get chest x-rays done at my regular vet and then take them with me for my specialist consultation. I like to do monitoring x-rays every six months or so in the moderate stages of heart disease.
Nothing, however, gives as much information as an echocardiogram. This shows condition of the valves, amount of regurgitation (blood flowing the wrong way as a result of defective valves), exact chamber sizes (versus x-rays which aren't as precise), a measurement of contractility (the pumping strength of the heart muscle), and it can also indicate the presence of pulmonary hypertension (high blood pressure in the vasculature of the lungs). An echo can usually be done less often than chest x-rays. Keep in mind that an echo is only as good as the person performing and interpreting the test. Some GP vets now do echos, but their lack of training and experience makes the test less useful than when performed by a specialist such as a board certified internal medicine specialist or a cardiologist. I believe that an echo done by a specialist is key to fine-tuning the most effective drug treatment plan - one that will give the most control of symptoms and the best chance at longevity.
If you use a specialist, he/she will likely do a diagnosis and treatment plan and then work with your regular vet for monitoring and dispensing of meds. This way you don't have to visit the specialist as often, particularly if there is a distance to travel. I wouldn't particularly recommend getting an echo at the upcoming heart clinic unless the cardiologist doing the echo is willing to follow up and work with your GP vet. The person doing the echo is really the person who should do the treatment plan so just taking the results to your vet won't give you the best outcome.
If you give me your location, I'd be happy to do a little investigation about what specialists might be within a reasonable driving distance.
Pat