Sometimes it can be a bit hard to tell because a dog can be so alert and actually fool a person into thinking he can hear (not on purpose of course!). So to test whether your dog is deaf you would need to make a noise, but make sure that the noise is not accompanied by air movement, by vibration of the floor or ground, or by some visual cue that your dog will respond to. Best to try this when your dog is not attentive to you and looking the other way. Best for you to be far enough away so that the noise is not making air movement or vibration. A suggestion is to try blowing a whistle at a distance your dog cannot feel a breeze from the whistle. If your dog acknowledges the noise, then he can hear. This is a pretty good test.
For an "official" test of a dog's hearing, there is a test that they do on breeds, such as dalmatians, that can have genetic deafness. This is the Baer Test - check out this link to learn more about this test: http://www.thedca.org/baerprimer.html
What do you mean by "has only one ear"? Do you mean only one ear flap or only one ear opening? Is this a birth defect or, if not, how did it happen?
Even hearing dogs will tend to focus more on hand commands if given the choice. Dogs are not language-oriented beings and are, thus, much more oriented to body language and hand signals. Thus, the fact that your dog is focused on your signals may not necessarily mean that she is deaf (but she could be).
Hope this is helpful!
Due to the fact that you clapped hands and tried other noises and she did not respond, it does indeed sound like she is deaf. That's great that you have already taught her hand signals. Like you, I usually speak also when hand signaling even though they cannot hear it (it just feels easier and more natural to me to also speak and maybe the dog can read me better if I do speak).
Being born with only one ear might be related to her deafness - not the fact that she has only one ear, but the fact that since she has one birth defect, that she might also tend to have another.
Check out the following book: "Living with a Deaf Dog - A book of advice, facts and experiences about canine deafness" by Susan Cope Becker. This book also gives further information on at home tests for deafness and on the Baer test. This book features a deaf English cocker spaniel named Spot on page 94 (English cocker spaniels have a relative high prevalence of deafness). The American cocker spaniel (listed as cocker spaniel) also is a breed with reported congenital deafness, but not as high prevalence as the English cocker. To find this book, try going to my web site: www.PersonalizedDogTraining.com and click on Doggy Marketplace at the upper left. Doggy Marketplace includes links to several dog book sellers.
Your veterinarian would have probably not caught your dog's deafness, unless he tested with the noises to see if she reacted or was able to perform the Baer test (which seems to only be done in certain specified clinics).
Good luck with your cocker spaniel.