Is it possible for me to apply for a student and working visa to obtain a post-graduate degree?
I don't think a higher national diploma (HND) degree is recognized as the equivalent of the bachelor's degree from a regular university. Consequently, it is unlikely you would be able to use it to gain entry to a master's program in either the US or Canada. 

I can't guarantee this is the way it works in Canada, but at least in the US, most students on visas have limited ability to work outside of the university, and certainly are unlikely to earn enough money to cover tuition as well as living expenses—the wages for typical student employment is on the order of $10/hour, and few students work more than about 20 hours per week. (That's approximately $10,000 per year.)