No, you should not be called a Certified Nursing Assistant. For one thing, you are not "certified" to my knowledge. Are you regulated by any body? Also, you are not performing any "nursing" actions. I greatly value all that PSWs do. You are excellent members of the health care team. However, you are not "almost" a nurse. You don't give meds or insert catheters as you do not have the knowledge, skill or judgement to do those nursing acts. Could you physically do the skill? Almost certainly. But being a nurse and being given the right to do those acts is far more involved than simply possessing the ability to them.
If you don't like your title, and want to do more, go back to school and bridge to nursing. Otherwise, be proud to be a PSW. Or refer to yourself as a Health Care Aide - in Ontario, that title is also sometimes used. You can also be called a UCP, or Unregulated Care Provider. But Ontario does not have Certified Nursing Assistants. You are not certified or regulated.
Sorry if I sound harsh, but your post rubbed me the wrong way, as it comes across as though you feel that you are almost a nurse because of the tasks you do. While as I said, I greatly value PSWs, you are not almost a nurse, and should not go around telling people that you do almost everything a nurse does, because that is simply not true.